Extra explanation: special cases | Wiskunde op Tilburg University

In this book you find the chain rule in three ways

composite power function: if $y(x)=(v(x))^p$ , then $y'(x)=(v(x))^{p-1}v'(x)$ .
composite exponential function: if $y(x)=a^{v(x)}$ , then $y'(x)=a^{v(x)}v'(x)\ln a$ .
composite logarithmic function: if $y(x)=\;^a\!\log (v(x))$ , then $y'(x)=\dfrac{v'(x)}{v(x) \ln a}$ .