Common Derivatives

\[f(x) = Constant, \: f'(x)=0\]

\[f(x)=x^n, \: f'(x) = nx^{n-1} \: provided: \: n \neq 0\]

\[f(x) = sin(ax), \: f'(x) = acos(ax) \: provided: a \neq 0\]

\[f(x) = cos(ax), \: f'(x) = -asin(ax) \: provided: a \neq 0\]

\[ln(x) = {1 \over x}\]

\[ln(u) = {u' \over u}, \: where \: u \: is \: a \: function \: of \: x\]