# How do you integrate #f(x)=(2x)/(x^3-7)# using the quotient rule?

##### 1 Answer

Nov 5, 2016

#### Explanation:

The quotient rule states that if

#f'(x)=(g'(x)h(x)-g(x)h'(x))/(h(x))^2# .

So, where

#f'(x)=(d/dx(2x)*(x^3-7)-2x*d/dx(x^3-7))/(x^3-7)^2#

Through the product rules:

#f'(x)=(2(x^3-7)-2x(3x^2))/(x^3-7)^2#

#f'(x)=(2x^3-14-6x^3)/(x^3-7)^2#

#f'(x)=-(4x^3+14)/(x^3-7)^2#