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) ((2-x)/(x^2+1)+2*x^3)

⇒ calculus.differentiation.plus

D(x) ((2-x)/(x^2+1))+D(x) (2*x^3)

⇒ calculus.differentiation.quotient

((x^2+1)*D(x) (2-x)-(2-x)*D(x) (x^2+1))/(x^2+1)^2+D(x) (2*x^3)

⇒ calculus.differentiation.deriv-of-poly

(-x^2-1-(2-x)*D(x) (x^2+1))/(x^2+1)^2+D(x) (2*x^3)

⇒ calculus.differentiation.deriv-of-poly

(-x^2-1-(2-x)*2*x)/(x^2+1)^2+D(x) (2*x^3)

⇒ calculus.differentiation.deriv-of-poly

(-x^2-1-(2-x)*2*x)/(x^2+1)^2+6*x^2

⇒ algebra.equations.linear.distr-times

(-x^2-1-4*x+2*x^2)/(x^2+1)^2+6*x^2

⇒ algebra.equations.linear.merge

(x^2-1-4*x)/(x^2+1)^2+6*x^2