Exponential Rules

\frac{d}{d x} (e^{x}) = e^{x} \frac{d}{d x} (e^{k x}) = k e^{k x} \frac{d}{d x} (a^{x}) = a^{x} ln a \frac{d}{d x} (a^{k x}) = a^{k x} (k ln a)

Logarithm Rules

\begin{array}{l} \frac{d}{dx}(\ln x) = \frac{1}{x} \\ \frac{d}{dx}(\ln kx) = \frac{1}{x} \\ \frac{d}{dx}(\ln(f(x))) = \frac{f'(x)}{f(x)} \\ \frac{d}{dx}(\log_a x) = \frac{1}{x \ln a} \end{array}