Exercise calculus.differentiation.quotient

Description
Use the quotient-rule to find the derivative of a polynomial. Only remove parentheses in the numerator.

Derivation

D(x) ((3-2*x)/(2*x^2-3)+x^3)

⇒ calculus.differentiation.plus

D(x) ((3-2*x)/(2*x^2-3))+D(x) (x^3)

⇒ 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+D(x) (x^3)

⇒ calculus.differentiation.deriv-of-poly

(-(2*x^2-3)*2-(3-2*x)*D(x) (2*x^2-3))/(2*x^2-3)^2+D(x) (x^3)

⇒ calculus.differentiation.deriv-of-poly

(-(2*x^2-3)*2-(3-2*x)*4*x)/(2*x^2-3)^2+D(x) (x^3)

⇒ calculus.differentiation.deriv-of-poly

(-(2*x^2-3)*2-(3-2*x)*4*x)/(2*x^2-3)^2+3*x^2

⇒ algebra.equations.linear.distr-times

(-4*x^2+6-(3-2*x)*4*x)/(2*x^2-3)^2+3*x^2

⇒ algebra.equations.linear.distr-times

(-4*x^2+6-12*x+8*x^2)/(2*x^2-3)^2+3*x^2

⇒ algebra.equations.linear.merge

(4*x^2+6-12*x)/(2*x^2-3)^2+3*x^2