A longer list of derivatives

(MathAcademy is having me review a lot of calc lately.)

$ \begin{array}{c|c} \text{Function / Rule} & \text{Derivative} \\ \hline c & 0 \\ x & 1 \\ cx & c \\ x^n & nx^{n-1} \\ c f(x) & c f'(x) \\ f(x) + g(x) & f'(x) + g'(x) \\ f(x) - g(x) & f'(x) - g'(x) \\ f(x)g(x) & f'(x)g(x) + f(x)g'(x) \\ \dfrac{f(x)}{g(x)} & \dfrac{f'(x)g(x) - f(x)g'(x)}{g(x)^2} \\ f(g(x)) & f'(g(x))g'(x) \\ e^x & e^x \\ e^u & e^u u' \\ a^x & a^x \ln a \\ a^u & a^u \ln(a) \cdot u' \\ \ln x & \dfrac{1}{x} \\ \ln u & \dfrac{u'}{u} \\ \log_a x & \dfrac{1}{x\ln a} \\ \sin x & \cos x \\ \cos x & -\sin x \\ \tan x & \sec^2 x \\ \sec x & \sec x \tan x \\ \csc x & -\csc x \cot x \\ \cot x & -\csc^2 x \\ \sin u & \cos u \cdot u' \\ \cos u & -\sin u \cdot u' \\ \tan u & \sec^2 u \cdot u' \\ \arcsin x & \dfrac{1}{\sqrt{1-x^2}} \\ \arccos x & -\dfrac{1}{\sqrt{1-x^2}} \\ \arctan x & \dfrac{1}{1+x^2} \end{array} $