Question

How do you find the derivative for `f(x) =x^6/(x-6)`?

Answer 1

`d/dx(x^6/(x-6))=(5x^6-36x^5)/(x-6)^2`

Explanation:

Using the quotient rule : `d/dx[f(x)/g(x)]=(g(x)*f'(x)-f(x)*g'(x))/(g(x))^2`, we get:

`d/dx(x^6/(x-6))=(6x^5(x-6)-x^6)/(x-6)^2`

`=(5x^6-36x^5)/(x-6)^2`