Question

Suppose that f is a function with f(-2)=-2 and f'(-2)=32. If h(x)=(1/(f(x)^5)) then h'(-2)=?

Answer 1

Use the chain rule:
\[h(x)=f(x)^{-5}\]
\[h'(x) = -5f(x)^{-6}f'(x)\]

Answer 2

Now just plug in -2:
h'(-2) = -5/(f(-2)^6) * f'(-2) = -5/64 * 32 = -5/2