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