Derivative_of_Function_to_Power_of_Function

Let $\map u x, \map v x$ be real functions which are differentiable on $\R$. Then $\map {\dfrac \d {\d x} } {u^v} = v u^{v - 1} \map {\dfrac \d {\d x} } u + u^v \paren {\ln u} \map {\dfrac \d {\d x} } v$