Rules of Differentiation

\frac{d}{d x} (k) = 0, where k is any constant

\frac{d}{d x} (x^{n}) = n x^{n - 1}

\frac{d}{d x} (e^{x}) = e^{x}

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

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

\frac{d}{d x} (\log_{a} x) = \frac{1}{(\ln a) x}

\frac{d}{d x} (f (x) \pm g (x)) = \frac{d}{d x} (f (x)) \pm \frac{d}{d x} (g (x))

\frac{d}{d x} (f (x) \cdot g (x)) = \frac{d}{d x} (f (x)) \cdot g (x) + f (x) \cdot \frac{d}{d x} (g (x))

\frac{d}{d x} (\frac{f (x)}{g (x)}) = \frac{\frac{d}{d x} (f (x)) \cdot g (x) - f (x) \cdot \frac{d}{d x} (g (x))}{{(g (x))}^{2}}

\frac{d}{d x} (g (f (x))) = g^{'} (f (x)) \cdot f^{'} (g (x))