Derivada de funciones exponenciales y logarítmicas

$\parbox{7cm}{ \begin{equation}\quad \frac{d}{dx}\ln{u}= \frac{1}... ...}\log_{a}{u}= \frac{\log_{a}{e}}{u} \frac{du}{dx}\\ a\neq 0,1 \end{equation}}$ $\parbox{8cm}{ \begin{equation}\quad \frac{d}{dx}a^u=a^u \ln{a}\f... ...{d}{dx}u^v = vu^{v-1} \frac{du}{dx}+ u^{v}\ln u \frac{dv}{dx} \end{equation}}$