Question

How do you differentiate `f(x)=(1/(x-3)^2)^2` using the chain rule?

Answer 1

Rewrite it as `f(x) = (x-3)^(-4)`

Explanation:

Apply the chain rule: `d/dx(u^-4) = -4u^-5 (du)/dx`

So `f'(x) = -4(x-3)^-5 d/dx(x-3)`

`= -4(x-3)^-5`

You may prefer to write the answer as `f'(x) = (-4)/(x-3)^5`