We defined log functions as inverses of exponentials:
\begin{eqnarray*} y = \ln(x) &\Longleftrightarrow & x =
e^y \cr y = \log_a(x) & \Longleftrightarrow & x = a^y.
\end{eqnarray*} Since we know how to differentiate exponentials,
we can use implicit differentiation to find the derivatives of
$\ln(x)$ and $\log_a(x)$. The videos below walk us through this
process.