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

\frac{d}{d x} (ln x) = \frac{1}{x} \frac{d}{d x} (ln k x) = \frac{1}{x}