Exercise calculus.differentiation
Description
Derivative
Derivations
1.
D(x) ((x^2+2*x)*(3*x+5))
⇒ calculus.differentiation.productD(x) (x^2+2*x)*(3*x+5)+(x^2+2*x)*D(x) (3*x+5)
⇒ calculus.differentiation.deriv-of-poly(2*x+2)*(3*x+5)+(x^2+2*x)*D(x) (3*x+5)
⇒ calculus.differentiation.deriv-of-poly(2*x+2)*(3*x+5)+(x^2+2*x)*3
2.
D(x) ((2*x^2-3*x)*(4*x+1))
⇒ calculus.differentiation.productD(x) (2*x^2-3*x)*(4*x+1)+(2*x^2-3*x)*D(x) (4*x+1)
⇒ calculus.differentiation.deriv-of-poly(4*x-3)*(4*x+1)+(2*x^2-3*x)*D(x) (4*x+1)
⇒ calculus.differentiation.deriv-of-poly(4*x-3)*(4*x+1)+(2*x^2-3*x)*4
3.
D(x) ((3*x^3+4*x)*(x^2-2))
⇒ calculus.differentiation.productD(x) (3*x^3+4*x)*(x^2-2)+(3*x^3+4*x)*D(x) (x^2-2)
⇒ calculus.differentiation.deriv-of-poly(9*x^2+4)*(x^2-2)+(3*x^3+4*x)*D(x) (x^2-2)
⇒ calculus.differentiation.deriv-of-poly(9*x^2+4)*(x^2-2)+(3*x^3+4*x)*2*x
4.
D(x) ((4*x^3-x)*(3*x^2+7*x))
⇒ calculus.differentiation.productD(x) (4*x^3-x)*(3*x^2+7*x)+(4*x^3-x)*D(x) (3*x^2+7*x)
⇒ calculus.differentiation.deriv-of-poly(12*x^2-1)*(3*x^2+7*x)+(4*x^3-x)*D(x) (3*x^2+7*x)
⇒ calculus.differentiation.deriv-of-poly(12*x^2-1)*(3*x^2+7*x)+(4*x^3-x)*(6*x+7)
5.
D(x) ((x^2+2*x)*(x^3-4*x^2+3))
⇒ calculus.differentiation.productD(x) (x^2+2*x)*(x^3-4*x^2+3)+(x^2+2*x)*D(x) (x^3-4*x^2+3)
⇒ calculus.differentiation.deriv-of-poly(2*x+2)*(x^3-4*x^2+3)+(x^2+2*x)*D(x) (x^3-4*x^2+3)
⇒ calculus.differentiation.deriv-of-poly(2*x+2)*(x^3-4*x^2+3)+(x^2+2*x)*(3*x^2-8*x)
6.
D(x) ((5*x-7)*(2*x^3-3*x+1))
⇒ calculus.differentiation.productD(x) (5*x-7)*(2*x^3-3*x+1)+(5*x-7)*D(x) (2*x^3-3*x+1)
⇒ calculus.differentiation.deriv-of-poly5*(2*x^3-3*x+1)+(5*x-7)*D(x) (2*x^3-3*x+1)
⇒ calculus.differentiation.deriv-of-poly5*(2*x^3-3*x+1)+(5*x-7)*(6*x^2-3)
7.
D(x) ((3*x^2+2)*(5*x^3+4*x^2-7*x))
⇒ calculus.differentiation.productD(x) (3*x^2+2)*(5*x^3+4*x^2-7*x)+(3*x^2+2)*D(x) (5*x^3+4*x^2-7*x)
⇒ calculus.differentiation.deriv-of-poly6*x*(5*x^3+4*x^2-7*x)+(3*x^2+2)*D(x) (5*x^3+4*x^2-7*x)
⇒ calculus.differentiation.deriv-of-poly6*x*(5*x^3+4*x^2-7*x)+(3*x^2+2)*(15*x^2+8*x-7)
8.
D(x) ((4*x+1)*(3*x^3-x^2+2*x))
⇒ calculus.differentiation.productD(x) (4*x+1)*(3*x^3-x^2+2*x)+(4*x+1)*D(x) (3*x^3-x^2+2*x)
⇒ calculus.differentiation.deriv-of-poly4*(3*x^3-x^2+2*x)+(4*x+1)*D(x) (3*x^3-x^2+2*x)
⇒ calculus.differentiation.deriv-of-poly4*(3*x^3-x^2+2*x)+(4*x+1)*(9*x^2-2*x+2)
9.
D(x) ((3*x+1)^2)
⇒ calculus.differentiation.chain-power2*(3*x+1)*D(x) (3*x+1)
⇒ calculus.differentiation.deriv-of-poly2*(3*x+1)*3
10.
D(x) ((5*x-2)^2)
⇒ calculus.differentiation.chain-power2*(5*x-2)*D(x) (5*x-2)
⇒ calculus.differentiation.deriv-of-poly2*(5*x-2)*5
11.
D(x) ((2*x+7)^2)
⇒ calculus.differentiation.chain-power2*(2*x+7)*D(x) (2*x+7)
⇒ calculus.differentiation.deriv-of-poly2*(2*x+7)*2
12.
D(x) ((4*x-3)^2)
⇒ calculus.differentiation.chain-power2*(4*x-3)*D(x) (4*x-3)
⇒ calculus.differentiation.deriv-of-poly2*(4*x-3)*4
13.
D(x) ((2*x^2-3*x)^2)
⇒ calculus.differentiation.chain-power2*(2*x^2-3*x)*D(x) (2*x^2-3*x)
⇒ calculus.differentiation.deriv-of-poly2*(2*x^2-3*x)*(4*x-3)
14.
D(x) ((3*x^2+2)^2)
⇒ calculus.differentiation.chain-power2*(3*x^2+2)*D(x) (3*x^2+2)
⇒ calculus.differentiation.deriv-of-poly2*(3*x^2+2)*6*x
15.
16.
D(x) ((5*x^3+7*x)^2)
⇒ calculus.differentiation.chain-power2*(5*x^3+7*x)*D(x) (5*x^3+7*x)
⇒ calculus.differentiation.deriv-of-poly2*(5*x^3+7*x)*(15*x^2+7)
17.
D(x) (5/(x-1))
⇒ calculus.differentiation.quotient((x-1)*D(x) 5-5*D(x) (x-1))/(x-1)^2
⇒ calculus.differentiation.deriv-of-poly-5*D(x) (x-1)/(x-1)^2
⇒ calculus.differentiation.deriv-of-poly-5/(x-1)^2
18.
D(x) (3/(x+2))
⇒ calculus.differentiation.quotient((x+2)*D(x) 3-3*D(x) (x+2))/(x+2)^2
⇒ calculus.differentiation.deriv-of-poly-3*D(x) (x+2)/(x+2)^2
⇒ calculus.differentiation.deriv-of-poly-3/(x+2)^2
19.
D(x) ((-2)/(x-3))
⇒ calculus.differentiation.quotient((x-3)*D(x) (-2)+2*D(x) (x-3))/(x-3)^2
⇒ calculus.differentiation.deriv-of-poly2*D(x) (x-3)/(x-3)^2
⇒ calculus.differentiation.deriv-of-poly2/(x-3)^2
20.
D(x) ((-3)/(x+4))
⇒ calculus.differentiation.quotient((x+4)*D(x) (-3)+3*D(x) (x+4))/(x+4)^2
⇒ calculus.differentiation.deriv-of-poly3*D(x) (x+4)/(x+4)^2
⇒ calculus.differentiation.deriv-of-poly3/(x+4)^2
21.
D(x) (3/(2*x-1))
⇒ calculus.differentiation.quotient((2*x-1)*D(x) 3-3*D(x) (2*x-1))/(2*x-1)^2
⇒ calculus.differentiation.deriv-of-poly-3*D(x) (2*x-1)/(2*x-1)^2
⇒ calculus.differentiation.deriv-of-poly-6/(2*x-1)^2
22.
D(x) (2/(3*x+4))
⇒ calculus.differentiation.quotient((3*x+4)*D(x) 2-2*D(x) (3*x+4))/(3*x+4)^2
⇒ calculus.differentiation.deriv-of-poly-2*D(x) (3*x+4)/(3*x+4)^2
⇒ calculus.differentiation.deriv-of-poly-6/(3*x+4)^2
23.
D(x) ((-4)/(3*x-1))
⇒ calculus.differentiation.quotient((3*x-1)*D(x) (-4)+4*D(x) (3*x-1))/(3*x-1)^2
⇒ calculus.differentiation.deriv-of-poly4*D(x) (3*x-1)/(3*x-1)^2
⇒ calculus.differentiation.deriv-of-poly12/(3*x-1)^2
24.
D(x) ((-2)/(4*x+3))
⇒ calculus.differentiation.quotient((4*x+3)*D(x) (-2)+2*D(x) (4*x+3))/(4*x+3)^2
⇒ calculus.differentiation.deriv-of-poly2*D(x) (4*x+3)/(4*x+3)^2
⇒ calculus.differentiation.deriv-of-poly8/(4*x+3)^2
25.
D(x) ((x+1)/(x-2))
⇒ calculus.differentiation.quotient((x-2)*D(x) (x+1)-(x+1)*D(x) (x-2))/(x-2)^2
⇒ calculus.differentiation.deriv-of-poly(x-2-(x+1)*D(x) (x-2))/(x-2)^2
⇒ calculus.differentiation.deriv-of-poly(x-2-x-1)/(x-2)^2
26.
D(x) ((x-3)/(x+4))
⇒ calculus.differentiation.quotient((x+4)*D(x) (x-3)-(x-3)*D(x) (x+4))/(x+4)^2
⇒ calculus.differentiation.deriv-of-poly(x+4-(x-3)*D(x) (x+4))/(x+4)^2
⇒ calculus.differentiation.deriv-of-poly(x+4-x+3)/(x+4)^2
27.
D(x) ((x+5)/(x-1))
⇒ calculus.differentiation.quotient((x-1)*D(x) (x+5)-(x+5)*D(x) (x-1))/(x-1)^2
⇒ calculus.differentiation.deriv-of-poly(x-1-(x+5)*D(x) (x-1))/(x-1)^2
⇒ calculus.differentiation.deriv-of-poly(x-1-x-5)/(x-1)^2
28.
D(x) ((x-2)/(x+1))
⇒ calculus.differentiation.quotient((x+1)*D(x) (x-2)-(x-2)*D(x) (x+1))/(x+1)^2
⇒ calculus.differentiation.deriv-of-poly(x+1-(x-2)*D(x) (x+1))/(x+1)^2
⇒ calculus.differentiation.deriv-of-poly(x+1-x+2)/(x+1)^2
29.
D(x) ((2*x+3)/(4*x-1))
⇒ calculus.differentiation.quotient((4*x-1)*D(x) (2*x+3)-(2*x+3)*D(x) (4*x-1))/(4*x-1)^2
⇒ calculus.differentiation.deriv-of-poly((4*x-1)*2-(2*x+3)*D(x) (4*x-1))/(4*x-1)^2
⇒ calculus.differentiation.deriv-of-poly((4*x-1)*2-(2*x+3)*4)/(4*x-1)^2
30.
D(x) ((3*x-1)/(2*x+1))
⇒ calculus.differentiation.quotient((2*x+1)*D(x) (3*x-1)-(3*x-1)*D(x) (2*x+1))/(2*x+1)^2
⇒ calculus.differentiation.deriv-of-poly((2*x+1)*3-(3*x-1)*D(x) (2*x+1))/(2*x+1)^2
⇒ calculus.differentiation.deriv-of-poly((2*x+1)*3-(3*x-1)*2)/(2*x+1)^2
31.
D(x) ((4*x+3)/(3*x-2))
⇒ calculus.differentiation.quotient((3*x-2)*D(x) (4*x+3)-(4*x+3)*D(x) (3*x-2))/(3*x-2)^2
⇒ calculus.differentiation.deriv-of-poly((3*x-2)*4-(4*x+3)*D(x) (3*x-2))/(3*x-2)^2
⇒ calculus.differentiation.deriv-of-poly((3*x-2)*4-(4*x+3)*3)/(3*x-2)^2
32.
D(x) ((5*x-2)/(3*x+4))
⇒ calculus.differentiation.quotient((3*x+4)*D(x) (5*x-2)-(5*x-2)*D(x) (3*x+4))/(3*x+4)^2
⇒ calculus.differentiation.deriv-of-poly((3*x+4)*5-(5*x-2)*D(x) (3*x+4))/(3*x+4)^2
⇒ calculus.differentiation.deriv-of-poly((3*x+4)*5-(5*x-2)*3)/(3*x+4)^2
33.
D(x) (3*x^2/(2*x^3+4))
⇒ calculus.differentiation.quotient((2*x^3+4)*D(x) (3*x^2)-3*x^2*D(x) (2*x^3+4))/(2*x^3+4)^2
⇒ calculus.differentiation.deriv-of-poly((2*x^3+4)*6*x-3*x^2*D(x) (2*x^3+4))/(2*x^3+4)^2
⇒ calculus.differentiation.deriv-of-poly((2*x^3+4)*6*x-18*x^4)/(2*x^3+4)^2
34.
D(x) (2*x^3/(3*x^2-1))
⇒ calculus.differentiation.quotient((3*x^2-1)*D(x) (2*x^3)-2*x^3*D(x) (3*x^2-1))/(3*x^2-1)^2
⇒ calculus.differentiation.deriv-of-poly((3*x^2-1)*6*x^2-2*x^3*D(x) (3*x^2-1))/(3*x^2-1)^2
⇒ calculus.differentiation.deriv-of-poly((3*x^2-1)*6*x^2-12*x^4)/(3*x^2-1)^2
35.
D(x) (x^2/(4*x^3-2))
⇒ calculus.differentiation.quotient((4*x^3-2)*D(x) (x^2)-x^2*D(x) (4*x^3-2))/(4*x^3-2)^2
⇒ calculus.differentiation.deriv-of-poly((4*x^3-2)*2*x-x^2*D(x) (4*x^3-2))/(4*x^3-2)^2
⇒ calculus.differentiation.deriv-of-poly((4*x^3-2)*2*x-12*x^4)/(4*x^3-2)^2
36.
D(x) (3*x^3/(5*x^2+7))
⇒ calculus.differentiation.quotient((5*x^2+7)*D(x) (3*x^3)-3*x^3*D(x) (5*x^2+7))/(5*x^2+7)^2
⇒ calculus.differentiation.deriv-of-poly((5*x^2+7)*9*x^2-3*x^3*D(x) (5*x^2+7))/(5*x^2+7)^2
⇒ calculus.differentiation.deriv-of-poly((5*x^2+7)*9*x^2-30*x^4)/(5*x^2+7)^2
37.
D(x) ((1-x^3)/(x+4))
⇒ calculus.differentiation.quotient((x+4)*D(x) (1-x^3)-(1-x^3)*D(x) (x+4))/(x+4)^2
⇒ calculus.differentiation.deriv-of-poly(-(x+4)*3*x^2-(1-x^3)*D(x) (x+4))/(x+4)^2
⇒ calculus.differentiation.deriv-of-poly(-(x+4)*3*x^2-1+x^3)/(x+4)^2
38.
D(x) ((x+3)/(2-x^2))
⇒ calculus.differentiation.quotient((2-x^2)*D(x) (x+3)-(x+3)*D(x) (2-x^2))/(2-x^2)^2
⇒ calculus.differentiation.deriv-of-poly(2-x^2-(x+3)*D(x) (2-x^2))/(2-x^2)^2
⇒ calculus.differentiation.deriv-of-poly(2-x^2+(x+3)*2*x)/(2-x^2)^2
39.
D(x) ((1-2*x^3)/(x+1))
⇒ calculus.differentiation.quotient((x+1)*D(x) (1-2*x^3)-(1-2*x^3)*D(x) (x+1))/(x+1)^2
⇒ calculus.differentiation.deriv-of-poly(-(x+1)*6*x^2-(1-2*x^3)*D(x) (x+1))/(x+1)^2
⇒ calculus.differentiation.deriv-of-poly(-(x+1)*6*x^2-1+2*x^3)/(x+1)^2
40.
D(x) ((x+5)/(2-3*x^2))
⇒ calculus.differentiation.quotient((2-3*x^2)*D(x) (x+5)-(x+5)*D(x) (2-3*x^2))/(2-3*x^2)^2
⇒ calculus.differentiation.deriv-of-poly(2-3*x^2-(x+5)*D(x) (2-3*x^2))/(2-3*x^2)^2
⇒ calculus.differentiation.deriv-of-poly(2-3*x^2+(x+5)*6*x)/(2-3*x^2)^2
41.
D(x) ((2-x)/(x^2+1)+2*x^3)
⇒ calculus.differentiation.plusD(x) ((2-x)/(x^2+1))+D(x) (2*x^3)
⇒ calculus.differentiation.deriv-of-polyD(x) ((2-x)/(x^2+1))+6*x^2
⇒ calculus.differentiation.quotient((x^2+1)*D(x) (2-x)-(2-x)*D(x) (x^2+1))/(x^2+1)^2+6*x^2
⇒ calculus.differentiation.deriv-of-poly(-x^2-1-(2-x)*D(x) (x^2+1))/(x^2+1)^2+6*x^2
⇒ calculus.differentiation.deriv-of-poly(-x^2-1-(2-x)*2*x)/(x^2+1)^2+6*x^2
42.
D(x) ((x^3-3)/(4-x)+x^2)
⇒ calculus.differentiation.plusD(x) ((x^3-3)/(4-x))+D(x) (x^2)
⇒ calculus.differentiation.deriv-of-polyD(x) ((x^3-3)/(4-x))+2*x
⇒ calculus.differentiation.quotient((4-x)*D(x) (x^3-3)-(x^3-3)*D(x) (4-x))/(4-x)^2+2*x
⇒ calculus.differentiation.deriv-of-poly((4-x)*3*x^2-(x^3-3)*D(x) (4-x))/(4-x)^2+2*x
⇒ calculus.differentiation.deriv-of-poly((4-x)*3*x^2+x^3-3)/(4-x)^2+2*x
43.
D(x) ((3-2*x)/(2*x^2-3)+x^3)
⇒ calculus.differentiation.plusD(x) ((3-2*x)/(2*x^2-3))+D(x) (x^3)
⇒ calculus.differentiation.deriv-of-polyD(x) ((3-2*x)/(2*x^2-3))+3*x^2
⇒ calculus.differentiation.quotient((2*x^2-3)*D(x) (3-2*x)-(3-2*x)*D(x) (2*x^2-3))/(2*x^2-3)^2+3*x^2
⇒ calculus.differentiation.deriv-of-poly(-(2*x^2-3)*2-(3-2*x)*D(x) (2*x^2-3))/(2*x^2-3)^2+3*x^2
⇒ calculus.differentiation.deriv-of-poly(-(2*x^2-3)*2-(3-2*x)*4*x)/(2*x^2-3)^2+3*x^2
44.
D(x) ((2*x^3-4)/(6-5*x)+4*x^2)
⇒ calculus.differentiation.plusD(x) ((2*x^3-4)/(6-5*x))+D(x) (4*x^2)
⇒ calculus.differentiation.deriv-of-polyD(x) ((2*x^3-4)/(6-5*x))+8*x
⇒ calculus.differentiation.quotient((6-5*x)*D(x) (2*x^3-4)-(2*x^3-4)*D(x) (6-5*x))/(6-5*x)^2+8*x
⇒ calculus.differentiation.deriv-of-poly((6-5*x)*6*x^2-(2*x^3-4)*D(x) (6-5*x))/(6-5*x)^2+8*x
⇒ calculus.differentiation.deriv-of-poly((6-5*x)*6*x^2+(2*x^3-4)*5)/(6-5*x)^2+8*x
45.
D(x) (4/x^2)
⇒ calculus.differentiation.quotient(x^2*D(x) 4-4*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly-4*D(x) (x^2)/x^4
⇒ calculus.differentiation.deriv-of-poly-8*x/x^4
46.
D(x) (5/x^3)
⇒ calculus.differentiation.quotient(x^3*D(x) 5-5*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly-5*D(x) (x^3)/x^6
⇒ calculus.differentiation.deriv-of-poly-15*x^2/x^6
47.
D(x) (2/x^4)
⇒ calculus.differentiation.quotient(x^4*D(x) 2-2*D(x) (x^4))/x^8
⇒ calculus.differentiation.deriv-of-poly-2*D(x) (x^4)/x^8
⇒ calculus.differentiation.deriv-of-poly-8*x^3/x^8
48.
D(x) (3/x^5)
⇒ calculus.differentiation.quotient(x^5*D(x) 3-3*D(x) (x^5))/x^10
⇒ calculus.differentiation.deriv-of-poly-3*D(x) (x^5)/x^10
⇒ calculus.differentiation.deriv-of-poly-15*x^4/x^10
49.
50.
51.
52.
53.
D(x) (3*x^2-4/x^2)
⇒ calculus.differentiation.minD(x) (3*x^2)-D(x) (4/x^2)
⇒ calculus.differentiation.deriv-of-poly6*x-D(x) (4/x^2)
⇒ calculus.differentiation.quotient6*x-(x^2*D(x) 4-4*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly6*x+4*D(x) (x^2)/x^4
⇒ calculus.differentiation.deriv-of-poly6*x+8*x/x^4
54.
D(x) (7*x^3-2/x^3)
⇒ calculus.differentiation.minD(x) (7*x^3)-D(x) (2/x^3)
⇒ calculus.differentiation.deriv-of-poly21*x^2-D(x) (2/x^3)
⇒ calculus.differentiation.quotient21*x^2-(x^3*D(x) 2-2*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly21*x^2+2*D(x) (x^3)/x^6
⇒ calculus.differentiation.deriv-of-poly21*x^2+6*x^2/x^6
55.
D(x) (2*x^4-5/x^4)
⇒ calculus.differentiation.minD(x) (2*x^4)-D(x) (5/x^4)
⇒ calculus.differentiation.deriv-of-poly8*x^3-D(x) (5/x^4)
⇒ calculus.differentiation.quotient8*x^3-(x^4*D(x) 5-5*D(x) (x^4))/x^8
⇒ calculus.differentiation.deriv-of-poly8*x^3+5*D(x) (x^4)/x^8
⇒ calculus.differentiation.deriv-of-poly8*x^3+20*x^3/x^8
56.
D(x) (2*x^5-6/x^5)
⇒ calculus.differentiation.minD(x) (2*x^5)-D(x) (6/x^5)
⇒ calculus.differentiation.deriv-of-poly10*x^4-D(x) (6/x^5)
⇒ calculus.differentiation.quotient10*x^4-(x^5*D(x) 6-6*D(x) (x^5))/x^10
⇒ calculus.differentiation.deriv-of-poly10*x^4+6*D(x) (x^5)/x^10
⇒ calculus.differentiation.deriv-of-poly10*x^4+30*x^4/x^10
57.
D(x) ((3*x+2)/x^3)
⇒ calculus.differentiation.quotient(x^3*D(x) (3*x+2)-(3*x+2)*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly(3*x^3-(3*x+2)*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly(3*x^3-(3*x+2)*3*x^2)/x^6
58.
D(x) ((2*x^2-4)/x^5)
⇒ calculus.differentiation.quotient(x^5*D(x) (2*x^2-4)-(2*x^2-4)*D(x) (x^5))/x^10
⇒ calculus.differentiation.deriv-of-poly(4*x^6-(2*x^2-4)*D(x) (x^5))/x^10
⇒ calculus.differentiation.deriv-of-poly(4*x^6-(2*x^2-4)*5*x^4)/x^10
59.
D(x) ((4*x-3)/x^2)
⇒ calculus.differentiation.quotient(x^2*D(x) (4*x-3)-(4*x-3)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(4*x^2-(4*x-3)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(4*x^2-(4*x-3)*2*x)/x^4
60.
D(x) ((6*x^2+5)/x^4)
⇒ calculus.differentiation.quotient(x^4*D(x) (6*x^2+5)-(6*x^2+5)*D(x) (x^4))/x^8
⇒ calculus.differentiation.deriv-of-poly(12*x^5-(6*x^2+5)*D(x) (x^4))/x^8
⇒ calculus.differentiation.deriv-of-poly(12*x^5-(6*x^2+5)*4*x^3)/x^8
61.
D(x) ((2*x^4+3)/x^2)
⇒ calculus.differentiation.quotient(x^2*D(x) (2*x^4+3)-(2*x^4+3)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(8*x^5-(2*x^4+3)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(8*x^5-(2*x^4+3)*2*x)/x^4
62.
D(x) ((2*x^5-5)/x^3)
⇒ calculus.differentiation.quotient(x^3*D(x) (2*x^5-5)-(2*x^5-5)*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly(10*x^7-(2*x^5-5)*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly(10*x^7-(2*x^5-5)*3*x^2)/x^6
63.
D(x) ((4*x^5-1)/x^2)
⇒ calculus.differentiation.quotient(x^2*D(x) (4*x^5-1)-(4*x^5-1)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(20*x^6-(4*x^5-1)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(20*x^6-(4*x^5-1)*2*x)/x^4
64.
D(x) ((4*x^4+3)/x^3)
⇒ calculus.differentiation.quotient(x^3*D(x) (4*x^4+3)-(4*x^4+3)*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly(16*x^6-(4*x^4+3)*D(x) (x^3))/x^6
⇒ calculus.differentiation.deriv-of-poly(16*x^6-(4*x^4+3)*3*x^2)/x^6
65.
D(x) ((3*x-1)/(7*x^2))
⇒ calculus.differentiation.quotient(7*x^2*D(x) (3*x-1)-(3*x-1)*D(x) (7*x^2))/(49*x^4)
⇒ calculus.differentiation.deriv-of-poly(21*x^2-(3*x-1)*D(x) (7*x^2))/(49*x^4)
⇒ calculus.differentiation.deriv-of-poly(21*x^2-(3*x-1)*14*x)/(49*x^4)
66.
D(x) ((2*x^3+1)/(3*x^4))
⇒ calculus.differentiation.quotient(3*x^4*D(x) (2*x^3+1)-(2*x^3+1)*D(x) (3*x^4))/(9*x^8)
⇒ calculus.differentiation.deriv-of-poly(18*x^6-(2*x^3+1)*D(x) (3*x^4))/(9*x^8)
⇒ calculus.differentiation.deriv-of-poly(18*x^6-(2*x^3+1)*12*x^3)/(9*x^8)
67.
D(x) ((x^2-2)/(3*x^3))
⇒ calculus.differentiation.quotient(3*x^3*D(x) (x^2-2)-(x^2-2)*D(x) (3*x^3))/(9*x^6)
⇒ calculus.differentiation.deriv-of-poly(6*x^4-(x^2-2)*D(x) (3*x^3))/(9*x^6)
⇒ calculus.differentiation.deriv-of-poly(6*x^4-(x^2-2)*9*x^2)/(9*x^6)
68.
D(x) ((x+5)/(6*x^3))
⇒ calculus.differentiation.quotient(6*x^3*D(x) (x+5)-(x+5)*D(x) (6*x^3))/(36*x^6)
⇒ calculus.differentiation.deriv-of-poly(6*x^3-(x+5)*D(x) (6*x^3))/(36*x^6)
⇒ calculus.differentiation.deriv-of-poly(6*x^3-(x+5)*18*x^2)/(36*x^6)
69.
D(x) (x*root x 3)
⇒ calculus.differentiation.productD(x) x*root x 3+x*D(x) (root x 3)
⇒ calculus.differentiation.deriv-of-polyroot x 3+x*D(x) (root x 3)
⇒ calculus.differentiation.def-rootroot x 3+x*D(x) (x^(1/3))
⇒ calculus.differentiation.chain-powerroot x 3+1/3*x*x^(-2/3)*D(x) x
⇒ calculus.differentiation.deriv-of-polyroot x 3+1/3*x*x^(-2/3)
70.
D(x) (x^3*sqrt x)
⇒ calculus.differentiation.productD(x) (x^3)*sqrt x+x^3*D(x) (sqrt x)
⇒ calculus.differentiation.deriv-of-poly3*x^2*sqrt x+x^3*D(x) (sqrt x)
⇒ calculus.differentiation.chain-sqrt3*x^2*sqrt x+x^3*(1/(2*sqrt x))*D(x) x
⇒ calculus.differentiation.deriv-of-poly3*x^2*sqrt x+x^3*(1/(2*sqrt x))
71.
D(x) (x*root x 5)
⇒ calculus.differentiation.productD(x) x*root x 5+x*D(x) (root x 5)
⇒ calculus.differentiation.deriv-of-polyroot x 5+x*D(x) (root x 5)
⇒ calculus.differentiation.def-rootroot x 5+x*D(x) (x^(1/5))
⇒ calculus.differentiation.chain-powerroot x 5+1/5*x*x^(-4/5)*D(x) x
⇒ calculus.differentiation.deriv-of-polyroot x 5+1/5*x*x^(-4/5)
72.
D(x) (x^4*sqrt x)
⇒ calculus.differentiation.productD(x) (x^4)*sqrt x+x^4*D(x) (sqrt x)
⇒ calculus.differentiation.deriv-of-poly4*x^3*sqrt x+x^4*D(x) (sqrt x)
⇒ calculus.differentiation.chain-sqrt4*x^3*sqrt x+x^4*(1/(2*sqrt x))*D(x) x
⇒ calculus.differentiation.deriv-of-poly4*x^3*sqrt x+x^4*(1/(2*sqrt x))
73.
D(x) (1/(x*root x 3))
⇒ calculus.differentiation.quotient(x*root x 3*D(x) 1-D(x) (x*root x 3))/(x*root x 3)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (x*root x 3)/(x*root x 3)^2
⇒ calculus.differentiation.product-(D(x) x*root x 3+x*D(x) (root x 3))/(x*root x 3)^2
⇒ calculus.differentiation.deriv-of-poly-(root x 3+x*D(x) (root x 3))/(x*root x 3)^2
⇒ calculus.differentiation.def-root-(root x 3+x*D(x) (x^(1/3)))/(x*root x 3)^2
⇒ calculus.differentiation.chain-power-(root x 3+1/3*x*x^(-2/3)*D(x) x)/(x*root x 3)^2
⇒ calculus.differentiation.deriv-of-poly-(root x 3+1/3*x*x^(-2/3))/(x*root x 3)^2
74.
D(x) (1/(x^3*sqrt x))
⇒ calculus.differentiation.quotient(x^3*sqrt x*D(x) 1-D(x) (x^3*sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (x^3*sqrt x)/(x^3*sqrt x)^2
⇒ calculus.differentiation.product-(D(x) (x^3)*sqrt x+x^3*D(x) (sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly-(3*x^2*sqrt x+x^3*D(x) (sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt-(3*x^2*sqrt x+x^3*(1/(2*sqrt x))*D(x) x)/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly-(3*x^2*sqrt x+x^3*(1/(2*sqrt x)))/(x^3*sqrt x)^2
75.
D(x) (1/(x*root x 5))
⇒ calculus.differentiation.quotient(x*root x 5*D(x) 1-D(x) (x*root x 5))/(x*root x 5)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (x*root x 5)/(x*root x 5)^2
⇒ calculus.differentiation.product-(D(x) x*root x 5+x*D(x) (root x 5))/(x*root x 5)^2
⇒ calculus.differentiation.deriv-of-poly-(root x 5+x*D(x) (root x 5))/(x*root x 5)^2
⇒ calculus.differentiation.def-root-(root x 5+x*D(x) (x^(1/5)))/(x*root x 5)^2
⇒ calculus.differentiation.chain-power-(root x 5+1/5*x*x^(-4/5)*D(x) x)/(x*root x 5)^2
⇒ calculus.differentiation.deriv-of-poly-(root x 5+1/5*x*x^(-4/5))/(x*root x 5)^2
76.
D(x) (1/(x^4*sqrt x))
⇒ calculus.differentiation.quotient(x^4*sqrt x*D(x) 1-D(x) (x^4*sqrt x))/(x^4*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (x^4*sqrt x)/(x^4*sqrt x)^2
⇒ calculus.differentiation.product-(D(x) (x^4)*sqrt x+x^4*D(x) (sqrt x))/(x^4*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly-(4*x^3*sqrt x+x^4*D(x) (sqrt x))/(x^4*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt-(4*x^3*sqrt x+x^4*(1/(2*sqrt x))*D(x) x)/(x^4*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly-(4*x^3*sqrt x+x^4*(1/(2*sqrt x)))/(x^4*sqrt x)^2
77.
D(x) (x^2*root (x^2) 3)
⇒ calculus.differentiation.productD(x) (x^2)*root (x^2) 3+x^2*D(x) (root (x^2) 3)
⇒ calculus.differentiation.deriv-of-poly2*x*root (x^2) 3+x^2*D(x) (root (x^2) 3)
⇒ calculus.differentiation.def-root2*x*root (x^2) 3+x^2*D(x) ((x^2)^(1/3))
⇒ calculus.differentiation.chain-power2*x*root (x^2) 3+1/3*x^2*(x^2)^(-2/3)*D(x) (x^2)
⇒ calculus.differentiation.deriv-of-poly2*x*root (x^2) 3+1/3*x^2*(x^2)^(-2/3)*2*x
78.
D(x) (x*root (x^3) 4)
⇒ calculus.differentiation.productD(x) x*root (x^3) 4+x*D(x) (root (x^3) 4)
⇒ calculus.differentiation.deriv-of-polyroot (x^3) 4+x*D(x) (root (x^3) 4)
⇒ calculus.differentiation.def-rootroot (x^3) 4+x*D(x) ((x^3)^(1/4))
⇒ calculus.differentiation.chain-powerroot (x^3) 4+1/4*x*(x^3)^(-3/4)*D(x) (x^3)
⇒ calculus.differentiation.deriv-of-polyroot (x^3) 4+1/4*x*(x^3)^(-3/4)*3*x^2
79.
D(x) (x^3*root (x^2) 5)
⇒ calculus.differentiation.productD(x) (x^3)*root (x^2) 5+x^3*D(x) (root (x^2) 5)
⇒ calculus.differentiation.deriv-of-poly3*x^2*root (x^2) 5+x^3*D(x) (root (x^2) 5)
⇒ calculus.differentiation.def-root3*x^2*root (x^2) 5+x^3*D(x) ((x^2)^(1/5))
⇒ calculus.differentiation.chain-power3*x^2*root (x^2) 5+1/5*x^3*(x^2)^(-4/5)*D(x) (x^2)
⇒ calculus.differentiation.deriv-of-poly3*x^2*root (x^2) 5+1/5*x^3*(x^2)^(-4/5)*2*x
80.
D(x) (x^2*root (x^3) 5)
⇒ calculus.differentiation.productD(x) (x^2)*root (x^3) 5+x^2*D(x) (root (x^3) 5)
⇒ calculus.differentiation.deriv-of-poly2*x*root (x^3) 5+x^2*D(x) (root (x^3) 5)
⇒ calculus.differentiation.def-root2*x*root (x^3) 5+x^2*D(x) ((x^3)^(1/5))
⇒ calculus.differentiation.chain-power2*x*root (x^3) 5+1/5*x^2*(x^3)^(-4/5)*D(x) (x^3)
⇒ calculus.differentiation.deriv-of-poly2*x*root (x^3) 5+1/5*x^2*(x^3)^(-4/5)*3*x^2
81.
D(x) ((x^3+1)*(2+sqrt x))
⇒ calculus.differentiation.productD(x) (x^3+1)*(2+sqrt x)+(x^3+1)*D(x) (2+sqrt x)
⇒ calculus.differentiation.deriv-of-poly3*x^2*(2+sqrt x)+(x^3+1)*D(x) (2+sqrt x)
⇒ calculus.differentiation.plus3*x^2*(2+sqrt x)+(x^3+1)*(D(x) 2+D(x) (sqrt x))
⇒ calculus.differentiation.deriv-of-poly3*x^2*(2+sqrt x)+(x^3+1)*D(x) (sqrt x)
⇒ calculus.differentiation.chain-sqrt3*x^2*(2+sqrt x)+(x^3+1)*(1/(2*sqrt x))*D(x) x
⇒ calculus.differentiation.deriv-of-poly3*x^2*(2+sqrt x)+(x^3+1)*(1/(2*sqrt x))
82.
D(x) ((3+x^2)*(1+root x 3))
⇒ calculus.differentiation.productD(x) (3+x^2)*(1+root x 3)+(3+x^2)*D(x) (1+root x 3)
⇒ calculus.differentiation.deriv-of-poly2*x*(1+root x 3)+(3+x^2)*D(x) (1+root x 3)
⇒ calculus.differentiation.plus2*x*(1+root x 3)+(3+x^2)*(D(x) 1+D(x) (root x 3))
⇒ calculus.differentiation.deriv-of-poly2*x*(1+root x 3)+(3+x^2)*D(x) (root x 3)
⇒ calculus.differentiation.def-root2*x*(1+root x 3)+(3+x^2)*D(x) (x^(1/3))
⇒ calculus.differentiation.chain-power2*x*(1+root x 3)+(3+x^2)*(1/3)*x^(-2/3)*D(x) x
⇒ calculus.differentiation.deriv-of-poly2*x*(1+root x 3)+(3+x^2)*(1/3)*x^(-2/3)
83.
D(x) ((x^2+1)*(root x 3+2))
⇒ calculus.differentiation.productD(x) (x^2+1)*(root x 3+2)+(x^2+1)*D(x) (root x 3+2)
⇒ calculus.differentiation.deriv-of-poly2*x*(root x 3+2)+(x^2+1)*D(x) (root x 3+2)
⇒ calculus.differentiation.plus2*x*(root x 3+2)+(x^2+1)*(D(x) (root x 3)+D(x) 2)
⇒ calculus.differentiation.deriv-of-poly2*x*(root x 3+2)+(x^2+1)*D(x) (root x 3)
⇒ calculus.differentiation.def-root2*x*(root x 3+2)+(x^2+1)*D(x) (x^(1/3))
⇒ calculus.differentiation.chain-power2*x*(root x 3+2)+(x^2+1)*(1/3)*x^(-2/3)*D(x) x
⇒ calculus.differentiation.deriv-of-poly2*x*(root x 3+2)+(x^2+1)*(1/3)*x^(-2/3)
84.
D(x) ((3+x^3)*(sqrt x+1))
⇒ calculus.differentiation.productD(x) (3+x^3)*(sqrt x+1)+(3+x^3)*D(x) (sqrt x+1)
⇒ calculus.differentiation.deriv-of-poly3*x^2*(sqrt x+1)+(3+x^3)*D(x) (sqrt x+1)
⇒ calculus.differentiation.plus3*x^2*(sqrt x+1)+(3+x^3)*(D(x) (sqrt x)+D(x) 1)
⇒ calculus.differentiation.deriv-of-poly3*x^2*(sqrt x+1)+(3+x^3)*D(x) (sqrt x)
⇒ calculus.differentiation.chain-sqrt3*x^2*(sqrt x+1)+(3+x^3)*(1/(2*sqrt x))*D(x) x
⇒ calculus.differentiation.deriv-of-poly3*x^2*(sqrt x+1)+(3+x^3)*(1/(2*sqrt x))
85.
D(x) ((sqrt x+1)^2)
⇒ calculus.differentiation.chain-power2*(sqrt x+1)*D(x) (sqrt x+1)
⇒ calculus.differentiation.plus2*(sqrt x+1)*(D(x) (sqrt x)+D(x) 1)
⇒ calculus.differentiation.deriv-of-poly2*(sqrt x+1)*D(x) (sqrt x)
⇒ calculus.differentiation.chain-sqrt2*(sqrt x+1)*(1/(2*sqrt x))*D(x) x
⇒ calculus.differentiation.deriv-of-poly2*(sqrt x+1)*(1/(2*sqrt x))
86.
D(x) ((x*sqrt x-3)^2)
⇒ calculus.differentiation.chain-power2*(x*sqrt x-3)*D(x) (x*sqrt x-3)
⇒ calculus.differentiation.min2*(x*sqrt x-3)*(D(x) (x*sqrt x)-D(x) 3)
⇒ calculus.differentiation.deriv-of-poly2*(x*sqrt x-3)*D(x) (x*sqrt x)
⇒ calculus.differentiation.product2*(x*sqrt x-3)*(D(x) x*sqrt x+x*D(x) (sqrt x))
⇒ calculus.differentiation.deriv-of-poly2*(x*sqrt x-3)*(sqrt x+x*D(x) (sqrt x))
⇒ calculus.differentiation.chain-sqrt2*(x*sqrt x-3)*(sqrt x+x*(1/(2*sqrt x))*D(x) x)
⇒ calculus.differentiation.deriv-of-poly2*(x*sqrt x-3)*(sqrt x+x*(1/(2*sqrt x)))
87.
D(x) ((sqrt x-2)^2)
⇒ calculus.differentiation.chain-power2*(sqrt x-2)*D(x) (sqrt x-2)
⇒ calculus.differentiation.min2*(sqrt x-2)*(D(x) (sqrt x)-D(x) 2)
⇒ calculus.differentiation.deriv-of-poly2*(sqrt x-2)*D(x) (sqrt x)
⇒ calculus.differentiation.chain-sqrt2*(sqrt x-2)*(1/(2*sqrt x))*D(x) x
⇒ calculus.differentiation.deriv-of-poly2*(sqrt x-2)*(1/(2*sqrt x))
88.
D(x) ((x*sqrt x+1)^2)
⇒ calculus.differentiation.chain-power2*(x*sqrt x+1)*D(x) (x*sqrt x+1)
⇒ calculus.differentiation.plus2*(x*sqrt x+1)*(D(x) (x*sqrt x)+D(x) 1)
⇒ calculus.differentiation.deriv-of-poly2*(x*sqrt x+1)*D(x) (x*sqrt x)
⇒ calculus.differentiation.product2*(x*sqrt x+1)*(D(x) x*sqrt x+x*D(x) (sqrt x))
⇒ calculus.differentiation.deriv-of-poly2*(x*sqrt x+1)*(sqrt x+x*D(x) (sqrt x))
⇒ calculus.differentiation.chain-sqrt2*(x*sqrt x+1)*(sqrt x+x*(1/(2*sqrt x))*D(x) x)
⇒ calculus.differentiation.deriv-of-poly2*(x*sqrt x+1)*(sqrt x+x*(1/(2*sqrt x)))
89.
D(x) ((x+2)/sqrt x)
⇒ calculus.differentiation.quotient(sqrt x*D(x) (x+2)-(x+2)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x+2)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.chain-sqrt(sqrt x-(x+2)*(1/(2*sqrt x))*D(x) x)/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x+2)*(1/(2*sqrt x)))/sqrt x^2
90.
D(x) ((x-3)/sqrt x)
⇒ calculus.differentiation.quotient(sqrt x*D(x) (x-3)-(x-3)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x-3)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.chain-sqrt(sqrt x-(x-3)*(1/(2*sqrt x))*D(x) x)/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x-3)*(1/(2*sqrt x)))/sqrt x^2
91.
D(x) ((x-4)/sqrt x)
⇒ calculus.differentiation.quotient(sqrt x*D(x) (x-4)-(x-4)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x-4)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.chain-sqrt(sqrt x-(x-4)*(1/(2*sqrt x))*D(x) x)/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x-4)*(1/(2*sqrt x)))/sqrt x^2
92.
D(x) ((x+5)/sqrt x)
⇒ calculus.differentiation.quotient(sqrt x*D(x) (x+5)-(x+5)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x+5)*D(x) (sqrt x))/sqrt x^2
⇒ calculus.differentiation.chain-sqrt(sqrt x-(x+5)*(1/(2*sqrt x))*D(x) x)/sqrt x^2
⇒ calculus.differentiation.deriv-of-poly(sqrt x-(x+5)*(1/(2*sqrt x)))/sqrt x^2
93.
D(x) ((x-2)/(x*sqrt x))
⇒ calculus.differentiation.quotient(x*sqrt x*D(x) (x-2)-(x-2)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x-2)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.product(x*sqrt x-(x-2)*(D(x) x*sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x-2)*(sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x*sqrt x-(x-2)*(sqrt x+x*(1/(2*sqrt x))*D(x) x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x-2)*(sqrt x+x*(1/(2*sqrt x))))/(x*sqrt x)^2
94.
D(x) ((x+3)/(x*sqrt x))
⇒ calculus.differentiation.quotient(x*sqrt x*D(x) (x+3)-(x+3)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x+3)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.product(x*sqrt x-(x+3)*(D(x) x*sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x+3)*(sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x*sqrt x-(x+3)*(sqrt x+x*(1/(2*sqrt x))*D(x) x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x+3)*(sqrt x+x*(1/(2*sqrt x))))/(x*sqrt x)^2
95.
D(x) ((x+4)/(x*sqrt x))
⇒ calculus.differentiation.quotient(x*sqrt x*D(x) (x+4)-(x+4)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x+4)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.product(x*sqrt x-(x+4)*(D(x) x*sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x+4)*(sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x*sqrt x-(x+4)*(sqrt x+x*(1/(2*sqrt x))*D(x) x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x+4)*(sqrt x+x*(1/(2*sqrt x))))/(x*sqrt x)^2
96.
D(x) ((x-5)/(x*sqrt x))
⇒ calculus.differentiation.quotient(x*sqrt x*D(x) (x-5)-(x-5)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x-5)*D(x) (x*sqrt x))/(x*sqrt x)^2
⇒ calculus.differentiation.product(x*sqrt x-(x-5)*(D(x) x*sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x-5)*(sqrt x+x*D(x) (sqrt x)))/(x*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x*sqrt x-(x-5)*(sqrt x+x*(1/(2*sqrt x))*D(x) x))/(x*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x*sqrt x-(x-5)*(sqrt x+x*(1/(2*sqrt x))))/(x*sqrt x)^2
97.
D(x) ((x^2+2)/(3*sqrt x))
⇒ calculus.differentiation.quotient(3*sqrt x*D(x) (x^2+2)-(x^2+2)*D(x) (3*sqrt x))/(3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(3*sqrt x*2*x-(x^2+2)*D(x) (3*sqrt x))/(3*sqrt x)^2
⇒ calculus.differentiation.constant-multiple(3*sqrt x*2*x-(x^2+2)*3*D(x) (sqrt x))/(3*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(3*sqrt x*2*x-(x^2+2)*3*(1/(2*sqrt x))*D(x) x)/(3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(3*sqrt x*2*x-(x^2+2)*3*(1/(2*sqrt x)))/(3*sqrt x)^2
98.
D(x) ((x^2-3)/(4*sqrt x))
⇒ calculus.differentiation.quotient(4*sqrt x*D(x) (x^2-3)-(x^2-3)*D(x) (4*sqrt x))/(4*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(4*sqrt x*2*x-(x^2-3)*D(x) (4*sqrt x))/(4*sqrt x)^2
⇒ calculus.differentiation.constant-multiple(4*sqrt x*2*x-(x^2-3)*4*D(x) (sqrt x))/(4*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(4*sqrt x*2*x-(x^2-3)*4*(1/(2*sqrt x))*D(x) x)/(4*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(4*sqrt x*2*x-(x^2-3)*4*(1/(2*sqrt x)))/(4*sqrt x)^2
99.
D(x) ((x^2+4)/(2*sqrt x))
⇒ calculus.differentiation.quotient(2*sqrt x*D(x) (x^2+4)-(x^2+4)*D(x) (2*sqrt x))/(2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(2*sqrt x*2*x-(x^2+4)*D(x) (2*sqrt x))/(2*sqrt x)^2
⇒ calculus.differentiation.constant-multiple(2*sqrt x*2*x-(x^2+4)*2*D(x) (sqrt x))/(2*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(2*sqrt x*2*x-(x^2+4)*2*(1/(2*sqrt x))*D(x) x)/(2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(2*sqrt x*2*x-(x^2+4)*2*(1/(2*sqrt x)))/(2*sqrt x)^2
100.
D(x) ((x^2-6)/(3*sqrt x))
⇒ calculus.differentiation.quotient(3*sqrt x*D(x) (x^2-6)-(x^2-6)*D(x) (3*sqrt x))/(3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(3*sqrt x*2*x-(x^2-6)*D(x) (3*sqrt x))/(3*sqrt x)^2
⇒ calculus.differentiation.constant-multiple(3*sqrt x*2*x-(x^2-6)*3*D(x) (sqrt x))/(3*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(3*sqrt x*2*x-(x^2-6)*3*(1/(2*sqrt x))*D(x) x)/(3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(3*sqrt x*2*x-(x^2-6)*3*(1/(2*sqrt x)))/(3*sqrt x)^2
101.
D(x) ((x+3)/(x^2*sqrt x))
⇒ calculus.differentiation.quotient(x^2*sqrt x*D(x) (x+3)-(x+3)*D(x) (x^2*sqrt x))/(x^2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^2*sqrt x-(x+3)*D(x) (x^2*sqrt x))/(x^2*sqrt x)^2
⇒ calculus.differentiation.product(x^2*sqrt x-(x+3)*(D(x) (x^2)*sqrt x+x^2*D(x) (sqrt x)))/(x^2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^2*sqrt x-(x+3)*(2*x*sqrt x+x^2*D(x) (sqrt x)))/(x^2*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x^2*sqrt x-(x+3)*(2*x*sqrt x+x^2*(1/(2*sqrt x))*D(x) x))/(x^2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^2*sqrt x-(x+3)*(2*x*sqrt x+x^2*(1/(2*sqrt x))))/(x^2*sqrt x)^2
102.
D(x) ((x-1)/(x^3*sqrt x))
⇒ calculus.differentiation.quotient(x^3*sqrt x*D(x) (x-1)-(x-1)*D(x) (x^3*sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^3*sqrt x-(x-1)*D(x) (x^3*sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.product(x^3*sqrt x-(x-1)*(D(x) (x^3)*sqrt x+x^3*D(x) (sqrt x)))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^3*sqrt x-(x-1)*(3*x^2*sqrt x+x^3*D(x) (sqrt x)))/(x^3*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x^3*sqrt x-(x-1)*(3*x^2*sqrt x+x^3*(1/(2*sqrt x))*D(x) x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^3*sqrt x-(x-1)*(3*x^2*sqrt x+x^3*(1/(2*sqrt x))))/(x^3*sqrt x)^2
103.
D(x) ((x-2)/(x^2*sqrt x))
⇒ calculus.differentiation.quotient(x^2*sqrt x*D(x) (x-2)-(x-2)*D(x) (x^2*sqrt x))/(x^2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^2*sqrt x-(x-2)*D(x) (x^2*sqrt x))/(x^2*sqrt x)^2
⇒ calculus.differentiation.product(x^2*sqrt x-(x-2)*(D(x) (x^2)*sqrt x+x^2*D(x) (sqrt x)))/(x^2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^2*sqrt x-(x-2)*(2*x*sqrt x+x^2*D(x) (sqrt x)))/(x^2*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x^2*sqrt x-(x-2)*(2*x*sqrt x+x^2*(1/(2*sqrt x))*D(x) x))/(x^2*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^2*sqrt x-(x-2)*(2*x*sqrt x+x^2*(1/(2*sqrt x))))/(x^2*sqrt x)^2
104.
D(x) ((x+4)/(x^3*sqrt x))
⇒ calculus.differentiation.quotient(x^3*sqrt x*D(x) (x+4)-(x+4)*D(x) (x^3*sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^3*sqrt x-(x+4)*D(x) (x^3*sqrt x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.product(x^3*sqrt x-(x+4)*(D(x) (x^3)*sqrt x+x^3*D(x) (sqrt x)))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^3*sqrt x-(x+4)*(3*x^2*sqrt x+x^3*D(x) (sqrt x)))/(x^3*sqrt x)^2
⇒ calculus.differentiation.chain-sqrt(x^3*sqrt x-(x+4)*(3*x^2*sqrt x+x^3*(1/(2*sqrt x))*D(x) x))/(x^3*sqrt x)^2
⇒ calculus.differentiation.deriv-of-poly(x^3*sqrt x-(x+4)*(3*x^2*sqrt x+x^3*(1/(2*sqrt x))))/(x^3*sqrt x)^2
105.
D(x) ((sqrt x-2)/x^2)
⇒ calculus.differentiation.quotient(x^2*D(x) (sqrt x-2)-(sqrt x-2)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(x^2*D(x) (sqrt x-2)-(sqrt x-2)*2*x)/x^4
⇒ calculus.differentiation.min(x^2*(D(x) (sqrt x)-D(x) 2)-(sqrt x-2)*2*x)/x^4
⇒ calculus.differentiation.deriv-of-poly(x^2*D(x) (sqrt x)-(sqrt x-2)*2*x)/x^4
⇒ calculus.differentiation.chain-sqrt(x^2*(1/(2*sqrt x))*D(x) x-(sqrt x-2)*2*x)/x^4
⇒ calculus.differentiation.deriv-of-poly(x^2*(1/(2*sqrt x))-(sqrt x-2)*2*x)/x^4
106.
D(x) ((2*sqrt x+1)/x^2)
⇒ calculus.differentiation.quotient(x^2*D(x) (2*sqrt x+1)-(2*sqrt x+1)*D(x) (x^2))/x^4
⇒ calculus.differentiation.deriv-of-poly(x^2*D(x) (2*sqrt x+1)-(2*sqrt x+1)*2*x)/x^4
⇒ calculus.differentiation.plus(x^2*(D(x) (2*sqrt x)+D(x) 1)-(2*sqrt x+1)*2*x)/x^4
⇒ calculus.differentiation.deriv-of-poly(x^2*D(x) (2*sqrt x)-(2*sqrt x+1)*2*x)/x^4
⇒ calculus.differentiation.constant-multiple(2*x^2*D(x) (sqrt x)-(2*sqrt x+1)*2*x)/x^4
⇒ calculus.differentiation.chain-sqrt(2*x^2*(1/(2*sqrt x))*D(x) x-(2*sqrt x+1)*2*x)/x^4
⇒ calculus.differentiation.deriv-of-poly(2*x^2*(1/(2*sqrt x))-(2*sqrt x+1)*2*x)/x^4
107.
D(x) ((1-sqrt x)/x)
⇒ calculus.differentiation.quotient(x*D(x) (1-sqrt x)-(1-sqrt x)*D(x) x)/x^2
⇒ calculus.differentiation.deriv-of-poly(x*D(x) (1-sqrt x)-1+sqrt x)/x^2
⇒ calculus.differentiation.min(x*(D(x) 1-D(x) (sqrt x))-1+sqrt x)/x^2
⇒ calculus.differentiation.deriv-of-poly(-x*D(x) (sqrt x)-1+sqrt x)/x^2
⇒ calculus.differentiation.chain-sqrt(-x*(1/(2*sqrt x))*D(x) x-1+sqrt x)/x^2
⇒ calculus.differentiation.deriv-of-poly(-x*(1/(2*sqrt x))-1+sqrt x)/x^2
108.
D(x) ((3*sqrt x+2)/x)
⇒ calculus.differentiation.quotient(x*D(x) (3*sqrt x+2)-(3*sqrt x+2)*D(x) x)/x^2
⇒ calculus.differentiation.deriv-of-poly(x*D(x) (3*sqrt x+2)-3*sqrt x-2)/x^2
⇒ calculus.differentiation.plus(x*(D(x) (3*sqrt x)+D(x) 2)-3*sqrt x-2)/x^2
⇒ calculus.differentiation.deriv-of-poly(x*D(x) (3*sqrt x)-3*sqrt x-2)/x^2
⇒ calculus.differentiation.constant-multiple(3*x*D(x) (sqrt x)-3*sqrt x-2)/x^2
⇒ calculus.differentiation.chain-sqrt(3*x*(1/(2*sqrt x))*D(x) x-3*sqrt x-2)/x^2
⇒ calculus.differentiation.deriv-of-poly(3*x*(1/(2*sqrt x))-3*sqrt x-2)/x^2
109.
D(x) (2*(x^2+3*x)^5)
⇒ calculus.differentiation.constant-multiple2*D(x) ((x^2+3*x)^5)
⇒ calculus.differentiation.chain-power10*(x^2+3*x)^4*D(x) (x^2+3*x)
⇒ calculus.differentiation.deriv-of-poly10*(x^2+3*x)^4*(2*x+3)
110.
D(x) (3*(x^3-4*x)^6)
⇒ calculus.differentiation.constant-multiple3*D(x) ((x^3-4*x)^6)
⇒ calculus.differentiation.chain-power18*(x^3-4*x)^5*D(x) (x^3-4*x)
⇒ calculus.differentiation.deriv-of-poly18*(x^3-4*x)^5*(3*x^2-4)
111.
D(x) (-6*(x^2+2*x)^4)
⇒ calculus.differentiation.negate-D(x) (6*(x^2+2*x)^4)
⇒ calculus.differentiation.constant-multiple-6*D(x) ((x^2+2*x)^4)
⇒ calculus.differentiation.chain-power-24*(x^2+2*x)^3*D(x) (x^2+2*x)
⇒ calculus.differentiation.deriv-of-poly-24*(x^2+2*x)^3*(2*x+2)
112.
D(x) (-5*(x^3-3*x^2)^3)
⇒ calculus.differentiation.negate-D(x) (5*(x^3-3*x^2)^3)
⇒ calculus.differentiation.constant-multiple-5*D(x) ((x^3-3*x^2)^3)
⇒ calculus.differentiation.chain-power-15*(x^3-3*x^2)^2*D(x) (x^3-3*x^2)
⇒ calculus.differentiation.deriv-of-poly-15*(x^3-3*x^2)^2*(3*x^2-6*x)
113.
D(x) (-2/(x^2+3*x)^5)
⇒ calculus.differentiation.negate-D(x) (2/(x^2+3*x)^5)
⇒ calculus.differentiation.quotient-((x^2+3*x)^5*D(x) 2-2*D(x) ((x^2+3*x)^5))/((x^2+3*x)^5)^2
⇒ calculus.differentiation.deriv-of-poly2*D(x) ((x^2+3*x)^5)/((x^2+3*x)^5)^2
⇒ calculus.differentiation.chain-power10*(x^2+3*x)^4*D(x) (x^2+3*x)/((x^2+3*x)^5)^2
⇒ calculus.differentiation.deriv-of-poly10*(x^2+3*x)^4*(2*x+3)/((x^2+3*x)^5)^2
114.
D(x) (-3/(x^3-4*x)^6)
⇒ calculus.differentiation.negate-D(x) (3/(x^3-4*x)^6)
⇒ calculus.differentiation.quotient-((x^3-4*x)^6*D(x) 3-3*D(x) ((x^3-4*x)^6))/((x^3-4*x)^6)^2
⇒ calculus.differentiation.deriv-of-poly3*D(x) ((x^3-4*x)^6)/((x^3-4*x)^6)^2
⇒ calculus.differentiation.chain-power18*(x^3-4*x)^5*D(x) (x^3-4*x)/((x^3-4*x)^6)^2
⇒ calculus.differentiation.deriv-of-poly18*(x^3-4*x)^5*(3*x^2-4)/((x^3-4*x)^6)^2
115.
D(x) (6/(x^2+2*x)^4)
⇒ calculus.differentiation.quotient((x^2+2*x)^4*D(x) 6-6*D(x) ((x^2+2*x)^4))/((x^2+2*x)^4)^2
⇒ calculus.differentiation.deriv-of-poly-6*D(x) ((x^2+2*x)^4)/((x^2+2*x)^4)^2
⇒ calculus.differentiation.chain-power-24*(x^2+2*x)^3*D(x) (x^2+2*x)/((x^2+2*x)^4)^2
⇒ calculus.differentiation.deriv-of-poly-24*(x^2+2*x)^3*(2*x+2)/((x^2+2*x)^4)^2
116.
D(x) (5/(x^3-3*x^2)^3)
⇒ calculus.differentiation.quotient((x^3-3*x^2)^3*D(x) 5-5*D(x) ((x^3-3*x^2)^3))/((x^3-3*x^2)^3)^2
⇒ calculus.differentiation.deriv-of-poly-5*D(x) ((x^3-3*x^2)^3)/((x^3-3*x^2)^3)^2
⇒ calculus.differentiation.chain-power-15*(x^3-3*x^2)^2*D(x) (x^3-3*x^2)/((x^3-3*x^2)^3)^2
⇒ calculus.differentiation.deriv-of-poly-15*(x^3-3*x^2)^2*(3*x^2-6*x)/((x^3-3*x^2)^3)^2
117.
D(x) (sqrt (3*x^4-x))
⇒ calculus.differentiation.chain-sqrt1/(2*sqrt (3*x^4-x))*D(x) (3*x^4-x)
⇒ calculus.differentiation.deriv-of-poly1/(2*sqrt (3*x^4-x))*(12*x^3-1)
118.
D(x) (sqrt (x^3+5*x^2))
⇒ calculus.differentiation.chain-sqrt1/(2*sqrt (x^3+5*x^2))*D(x) (x^3+5*x^2)
⇒ calculus.differentiation.deriv-of-poly1/(2*sqrt (x^3+5*x^2))*(3*x^2+10*x)
119.
D(x) (sqrt (6*x^2+x))
⇒ calculus.differentiation.chain-sqrt1/(2*sqrt (6*x^2+x))*D(x) (6*x^2+x)
⇒ calculus.differentiation.deriv-of-poly1/(2*sqrt (6*x^2+x))*(12*x+1)
120.
D(x) (sqrt (7*x^3-3*x^2))
⇒ calculus.differentiation.chain-sqrt1/(2*sqrt (7*x^3-3*x^2))*D(x) (7*x^3-3*x^2)
⇒ calculus.differentiation.deriv-of-poly1/(2*sqrt (7*x^3-3*x^2))*(21*x^2-6*x)
121.
D(x) (1/sqrt (3*x-2))
⇒ calculus.differentiation.quotient(sqrt (3*x-2)*D(x) 1-D(x) (sqrt (3*x-2)))/sqrt (3*x-2)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (sqrt (3*x-2))/sqrt (3*x-2)^2
⇒ calculus.differentiation.chain-sqrt-1/(2*sqrt (3*x-2))*D(x) (3*x-2)/sqrt (3*x-2)^2
⇒ calculus.differentiation.deriv-of-poly-1/(2*sqrt (3*x-2))*3/sqrt (3*x-2)^2
122.
D(x) (1/sqrt (8*x+5))
⇒ calculus.differentiation.quotient(sqrt (8*x+5)*D(x) 1-D(x) (sqrt (8*x+5)))/sqrt (8*x+5)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (sqrt (8*x+5))/sqrt (8*x+5)^2
⇒ calculus.differentiation.chain-sqrt-1/(2*sqrt (8*x+5))*D(x) (8*x+5)/sqrt (8*x+5)^2
⇒ calculus.differentiation.deriv-of-poly-1/(2*sqrt (8*x+5))*8/sqrt (8*x+5)^2
123.
D(x) (1/sqrt (3*x-4))
⇒ calculus.differentiation.quotient(sqrt (3*x-4)*D(x) 1-D(x) (sqrt (3*x-4)))/sqrt (3*x-4)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (sqrt (3*x-4))/sqrt (3*x-4)^2
⇒ calculus.differentiation.chain-sqrt-1/(2*sqrt (3*x-4))*D(x) (3*x-4)/sqrt (3*x-4)^2
⇒ calculus.differentiation.deriv-of-poly-1/(2*sqrt (3*x-4))*3/sqrt (3*x-4)^2
124.
D(x) (1/sqrt (5*x-2))
⇒ calculus.differentiation.quotient(sqrt (5*x-2)*D(x) 1-D(x) (sqrt (5*x-2)))/sqrt (5*x-2)^2
⇒ calculus.differentiation.deriv-of-poly-D(x) (sqrt (5*x-2))/sqrt (5*x-2)^2
⇒ calculus.differentiation.chain-sqrt-1/(2*sqrt (5*x-2))*D(x) (5*x-2)/sqrt (5*x-2)^2
⇒ calculus.differentiation.deriv-of-poly-1/(2*sqrt (5*x-2))*5/sqrt (5*x-2)^2
125.
D(x) ((2*x-1)^2*sqrt (2*x-1))
⇒ calculus.differentiation.productD(x) ((2*x-1)^2)*sqrt (2*x-1)+(2*x-1)^2*D(x) (sqrt (2*x-1))
⇒ calculus.differentiation.chain-power2*(2*x-1)*D(x) (2*x-1)*sqrt (2*x-1)+(2*x-1)^2*D(x) (sqrt (2*x-1))
⇒ calculus.differentiation.deriv-of-poly2*(2*x-1)*2*sqrt (2*x-1)+(2*x-1)^2*D(x) (sqrt (2*x-1))
⇒ calculus.differentiation.chain-sqrt2*(2*x-1)*2*sqrt (2*x-1)+(2*x-1)^2*(1/(2*sqrt (2*x-1)))*D(x) (2*x-1)
⇒ calculus.differentiation.deriv-of-poly2*(2*x-1)*2*sqrt (2*x-1)+(2*x-1)^2*(1/(2*sqrt (2*x-1)))*2
126.
D(x) ((3*x^2+2)*sqrt (3*x^2+2))
⇒ calculus.differentiation.productD(x) (3*x^2+2)*sqrt (3*x^2+2)+(3*x^2+2)*D(x) (sqrt (3*x^2+2))
⇒ calculus.differentiation.deriv-of-poly6*x*sqrt (3*x^2+2)+(3*x^2+2)*D(x) (sqrt (3*x^2+2))
⇒ calculus.differentiation.chain-sqrt6*x*sqrt (3*x^2+2)+(3*x^2+2)*(1/(2*sqrt (3*x^2+2)))*D(x) (3*x^2+2)
⇒ calculus.differentiation.deriv-of-poly6*x*sqrt (3*x^2+2)+(3*x^2+2)*(1/(2*sqrt (3*x^2+2)))*6*x
127.
D(x) ((3*x+5)^3*sqrt (3*x+5))
⇒ calculus.differentiation.productD(x) ((3*x+5)^3)*sqrt (3*x+5)+(3*x+5)^3*D(x) (sqrt (3*x+5))
⇒ calculus.differentiation.chain-power3*(3*x+5)^2*D(x) (3*x+5)*sqrt (3*x+5)+(3*x+5)^3*D(x) (sqrt (3*x+5))
⇒ calculus.differentiation.deriv-of-poly3*(3*x+5)^2*3*sqrt (3*x+5)+(3*x+5)^3*D(x) (sqrt (3*x+5))
⇒ calculus.differentiation.chain-sqrt3*(3*x+5)^2*3*sqrt (3*x+5)+(3*x+5)^3*(1/(2*sqrt (3*x+5)))*D(x) (3*x+5)
⇒ calculus.differentiation.deriv-of-poly3*(3*x+5)^2*3*sqrt (3*x+5)+(3*x+5)^3*(1/(2*sqrt (3*x+5)))*3
128.
D(x) ((4*x^3-7)*sqrt (4*x^3-7))
⇒ calculus.differentiation.productD(x) (4*x^3-7)*sqrt (4*x^3-7)+(4*x^3-7)*D(x) (sqrt (4*x^3-7))
⇒ calculus.differentiation.deriv-of-poly12*x^2*sqrt (4*x^3-7)+(4*x^3-7)*D(x) (sqrt (4*x^3-7))
⇒ calculus.differentiation.chain-sqrt12*x^2*sqrt (4*x^3-7)+(4*x^3-7)*(1/(2*sqrt (4*x^3-7)))*D(x) (4*x^3-7)
⇒ calculus.differentiation.deriv-of-poly12*x^2*sqrt (4*x^3-7)+(4*x^3-7)*(1/(2*sqrt (4*x^3-7)))*12*x^2
129.
D(x) (2*x*sqrt (4*x+3))
⇒ calculus.differentiation.productD(x) (2*x)*sqrt (4*x+3)+2*x*D(x) (sqrt (4*x+3))
⇒ calculus.differentiation.deriv-of-poly2*sqrt (4*x+3)+2*x*D(x) (sqrt (4*x+3))
⇒ calculus.differentiation.chain-sqrt2*sqrt (4*x+3)+2*x*(1/(2*sqrt (4*x+3)))*D(x) (4*x+3)
⇒ calculus.differentiation.deriv-of-poly2*sqrt (4*x+3)+2*x*(1/(2*sqrt (4*x+3)))*4
130.
D(x) (3*x*sqrt (2*x-5))
⇒ calculus.differentiation.productD(x) (3*x)*sqrt (2*x-5)+3*x*D(x) (sqrt (2*x-5))
⇒ calculus.differentiation.deriv-of-poly3*sqrt (2*x-5)+3*x*D(x) (sqrt (2*x-5))
⇒ calculus.differentiation.chain-sqrt3*sqrt (2*x-5)+3*x*(1/(2*sqrt (2*x-5)))*D(x) (2*x-5)
⇒ calculus.differentiation.deriv-of-poly3*sqrt (2*x-5)+3*x*(1/(2*sqrt (2*x-5)))*2
131.
D(x) (4*x*sqrt (3*x+2))
⇒ calculus.differentiation.productD(x) (4*x)*sqrt (3*x+2)+4*x*D(x) (sqrt (3*x+2))
⇒ calculus.differentiation.deriv-of-poly4*sqrt (3*x+2)+4*x*D(x) (sqrt (3*x+2))
⇒ calculus.differentiation.chain-sqrt4*sqrt (3*x+2)+4*x*(1/(2*sqrt (3*x+2)))*D(x) (3*x+2)
⇒ calculus.differentiation.deriv-of-poly4*sqrt (3*x+2)+4*x*(1/(2*sqrt (3*x+2)))*3
132.
D(x) (2*x*sqrt (5*x-3))
⇒ calculus.differentiation.productD(x) (2*x)*sqrt (5*x-3)+2*x*D(x) (sqrt (5*x-3))
⇒ calculus.differentiation.deriv-of-poly2*sqrt (5*x-3)+2*x*D(x) (sqrt (5*x-3))
⇒ calculus.differentiation.chain-sqrt2*sqrt (5*x-3)+2*x*(1/(2*sqrt (5*x-3)))*D(x) (5*x-3)
⇒ calculus.differentiation.deriv-of-poly2*sqrt (5*x-3)+2*x*(1/(2*sqrt (5*x-3)))*5
133.
D(x) (x^2*(4*x^2-2)^3)
⇒ calculus.differentiation.productD(x) (x^2)*(4*x^2-2)^3+x^2*D(x) ((4*x^2-2)^3)
⇒ calculus.differentiation.deriv-of-poly2*x*(4*x^2-2)^3+x^2*D(x) ((4*x^2-2)^3)
⇒ calculus.differentiation.chain-power2*x*(4*x^2-2)^3+3*x^2*(4*x^2-2)^2*D(x) (4*x^2-2)
⇒ calculus.differentiation.deriv-of-poly2*x*(4*x^2-2)^3+3*x^2*(4*x^2-2)^2*8*x
134.
D(x) (x^3*(3*x-4)^3)
⇒ calculus.differentiation.productD(x) (x^3)*(3*x-4)^3+x^3*D(x) ((3*x-4)^3)
⇒ calculus.differentiation.deriv-of-poly3*x^2*(3*x-4)^3+x^3*D(x) ((3*x-4)^3)
⇒ calculus.differentiation.chain-power3*x^2*(3*x-4)^3+3*x^3*(3*x-4)^2*D(x) (3*x-4)
⇒ calculus.differentiation.deriv-of-poly3*x^2*(3*x-4)^3+3*x^3*(3*x-4)^2*3
135.
D(x) (x^4*(3*x^2+1)^5)
⇒ calculus.differentiation.productD(x) (x^4)*(3*x^2+1)^5+x^4*D(x) ((3*x^2+1)^5)
⇒ calculus.differentiation.deriv-of-poly4*x^3*(3*x^2+1)^5+x^4*D(x) ((3*x^2+1)^5)
⇒ calculus.differentiation.chain-power4*x^3*(3*x^2+1)^5+5*x^4*(3*x^2+1)^4*D(x) (3*x^2+1)
⇒ calculus.differentiation.deriv-of-poly4*x^3*(3*x^2+1)^5+5*x^4*(3*x^2+1)^4*6*x
136.
D(x) (x^5*(4*x+3)^4)
⇒ calculus.differentiation.productD(x) (x^5)*(4*x+3)^4+x^5*D(x) ((4*x+3)^4)
⇒ calculus.differentiation.deriv-of-poly5*x^4*(4*x+3)^4+x^5*D(x) ((4*x+3)^4)
⇒ calculus.differentiation.chain-power5*x^4*(4*x+3)^4+4*x^5*(4*x+3)^3*D(x) (4*x+3)
⇒ calculus.differentiation.deriv-of-poly5*x^4*(4*x+3)^4+4*x^5*(4*x+3)^3*4
137.
D(x) ((x+3)/sqrt (2*x-1))
⇒ calculus.differentiation.quotient(sqrt (2*x-1)*D(x) (x+3)-(x+3)*D(x) (sqrt (2*x-1)))/sqrt (2*x-1)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (2*x-1)-(x+3)*D(x) (sqrt (2*x-1)))/sqrt (2*x-1)^2
⇒ calculus.differentiation.chain-sqrt(sqrt (2*x-1)-(x+3)*(1/(2*sqrt (2*x-1)))*D(x) (2*x-1))/sqrt (2*x-1)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (2*x-1)-(x+3)*(1/(2*sqrt (2*x-1)))*2)/sqrt (2*x-1)^2
138.
D(x) ((x+7)/sqrt (4*x+3))
⇒ calculus.differentiation.quotient(sqrt (4*x+3)*D(x) (x+7)-(x+7)*D(x) (sqrt (4*x+3)))/sqrt (4*x+3)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (4*x+3)-(x+7)*D(x) (sqrt (4*x+3)))/sqrt (4*x+3)^2
⇒ calculus.differentiation.chain-sqrt(sqrt (4*x+3)-(x+7)*(1/(2*sqrt (4*x+3)))*D(x) (4*x+3))/sqrt (4*x+3)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (4*x+3)-(x+7)*(1/(2*sqrt (4*x+3)))*4)/sqrt (4*x+3)^2
139.
D(x) ((x-2)/sqrt (3*x+1))
⇒ calculus.differentiation.quotient(sqrt (3*x+1)*D(x) (x-2)-(x-2)*D(x) (sqrt (3*x+1)))/sqrt (3*x+1)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (3*x+1)-(x-2)*D(x) (sqrt (3*x+1)))/sqrt (3*x+1)^2
⇒ calculus.differentiation.chain-sqrt(sqrt (3*x+1)-(x-2)*(1/(2*sqrt (3*x+1)))*D(x) (3*x+1))/sqrt (3*x+1)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (3*x+1)-(x-2)*(1/(2*sqrt (3*x+1)))*3)/sqrt (3*x+1)^2
140.
D(x) ((x-7)/sqrt (5*x-4))
⇒ calculus.differentiation.quotient(sqrt (5*x-4)*D(x) (x-7)-(x-7)*D(x) (sqrt (5*x-4)))/sqrt (5*x-4)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (5*x-4)-(x-7)*D(x) (sqrt (5*x-4)))/sqrt (5*x-4)^2
⇒ calculus.differentiation.chain-sqrt(sqrt (5*x-4)-(x-7)*(1/(2*sqrt (5*x-4)))*D(x) (5*x-4))/sqrt (5*x-4)^2
⇒ calculus.differentiation.deriv-of-poly(sqrt (5*x-4)-(x-7)*(1/(2*sqrt (5*x-4)))*5)/sqrt (5*x-4)^2
141.
D(x) (sqrt (2*x^2-1)/(x+3))
⇒ calculus.differentiation.quotient((x+3)*D(x) (sqrt (2*x^2-1))-sqrt (2*x^2-1)*D(x) (x+3))/(x+3)^2
⇒ calculus.differentiation.deriv-of-poly((x+3)*D(x) (sqrt (2*x^2-1))-sqrt (2*x^2-1))/(x+3)^2
⇒ calculus.differentiation.chain-sqrt((x+3)*(1/(2*sqrt (2*x^2-1)))*D(x) (2*x^2-1)-sqrt (2*x^2-1))/(x+3)^2
⇒ calculus.differentiation.deriv-of-poly((x+3)*(1/(2*sqrt (2*x^2-1)))*4*x-sqrt (2*x^2-1))/(x+3)^2
142.
D(x) (sqrt (4*x^2+3)/(x+7))
⇒ calculus.differentiation.quotient((x+7)*D(x) (sqrt (4*x^2+3))-sqrt (4*x^2+3)*D(x) (x+7))/(x+7)^2
⇒ calculus.differentiation.deriv-of-poly((x+7)*D(x) (sqrt (4*x^2+3))-sqrt (4*x^2+3))/(x+7)^2
⇒ calculus.differentiation.chain-sqrt((x+7)*(1/(2*sqrt (4*x^2+3)))*D(x) (4*x^2+3)-sqrt (4*x^2+3))/(x+7)^2
⇒ calculus.differentiation.deriv-of-poly((x+7)*(1/(2*sqrt (4*x^2+3)))*8*x-sqrt (4*x^2+3))/(x+7)^2
143.
D(x) (sqrt (3*x^2+1)/(x-2))
⇒ calculus.differentiation.quotient((x-2)*D(x) (sqrt (3*x^2+1))-sqrt (3*x^2+1)*D(x) (x-2))/(x-2)^2
⇒ calculus.differentiation.deriv-of-poly((x-2)*D(x) (sqrt (3*x^2+1))-sqrt (3*x^2+1))/(x-2)^2
⇒ calculus.differentiation.chain-sqrt((x-2)*(1/(2*sqrt (3*x^2+1)))*D(x) (3*x^2+1)-sqrt (3*x^2+1))/(x-2)^2
⇒ calculus.differentiation.deriv-of-poly((x-2)*(1/(2*sqrt (3*x^2+1)))*6*x-sqrt (3*x^2+1))/(x-2)^2
144.
D(x) (sqrt (5*x^2-4)/(x-7))
⇒ calculus.differentiation.quotient((x-7)*D(x) (sqrt (5*x^2-4))-sqrt (5*x^2-4)*D(x) (x-7))/(x-7)^2
⇒ calculus.differentiation.deriv-of-poly((x-7)*D(x) (sqrt (5*x^2-4))-sqrt (5*x^2-4))/(x-7)^2
⇒ calculus.differentiation.chain-sqrt((x-7)*(1/(2*sqrt (5*x^2-4)))*D(x) (5*x^2-4)-sqrt (5*x^2-4))/(x-7)^2
⇒ calculus.differentiation.deriv-of-poly((x-7)*(1/(2*sqrt (5*x^2-4)))*10*x-sqrt (5*x^2-4))/(x-7)^2