Question

How do you differentiate `f(x)=(4x^6-3sqrt(x/(x-5)^2)+2)^2` using the chain rule?

Answer 1

`f'(x)=2(4*x^6-3sqrt(x/(x-5)^2)+2)*(24*x^5-3/(2*sqrt(x/(x-5)^2))((-x-5)/(x-5)^3))`

Explanation:

By the chain rule we get

`f'(x)=2(4x^6-3sqrt(x/(x-5)^2)+2)*(24*x^5-3/(2*sqrt(x/(x-5)^2))*(x-5-2x)/(x-5)^3))`