logarithmic differentiation, a function to the power of another function

Question

Let $f$, $g$ be two differentiable functions. Using logarithmic differentiation, find a formula for the derivative of $h(x) = f(x)^{g(x)}$.

Answer 1

$h(x)=e^{g(x)ln(f(x))}$ implies that $h'(x)=(g'(x)ln(f(x)+{{f'(x)}\over {f(x)}}g(x))e^{g(x)ln(f(x))}$