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

⇒ calculus.differentiation.plus

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

⇒ calculus.differentiation.quotient

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

⇒ calculus.differentiation.deriv-of-poly

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

⇒ calculus.differentiation.deriv-of-poly

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

⇒ calculus.differentiation.deriv-of-poly

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

⇒ algebra.equations.linear.distr-times

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

⇒ algebra.equations.linear.merge

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