## Calculus (3rd Edition)

$$g'(x)= -\frac{1}{5x^{6/5}} .$$
Since $f(x)=x^{-5}$, then $f'(x)=-5x^{-6}$. Hence by Theorem 2 and assuming that $g(x)=f^{-1}(x)$, we have $$g(x)= x^{-1/5}, \quad g'(x)=\frac{1}{f'(g(x))}=-\frac{1}{5x^{6/5}} .$$