Calculus I

Derivatives of Basic Functions

Functions	Derivatives
Power and logarithmic functions	$\displaystyle\frac{d}{dx} x^n = n x^{n-1}$ $\displaystyle\frac{d}{dx} \ln \vert x\vert = \frac{1}{x}$
Exponential functions	$\displaystyle\frac{d}{dx} e^x = e^x$
Trigonometric functions	$\displaystyle\frac{d}{dx} \sin x = \cos x$ $\displaystyle\frac{d}{dx} \cos x = -\sin x$ $\displaystyle\frac{d}{dx} \tan x = \frac{1}{\cos^2 x} = \sec^2 x$ $\displaystyle\frac{d}{dx} \cot x = -\frac{1}{\sin^2 x} = -\csc^2 x$ $\displaystyle\frac{d}{dx} \sec x = \sec x \tan x$ $\displaystyle\frac{d}{dx} \csc x = -\csc x \cot x$
Hyperbolic functions	$\displaystyle\frac{d}{dx} \sinh x = \cosh x$ $\displaystyle\frac{d}{dx} \cosh x = \sinh x$ $\displaystyle\frac{d}{dx} \tanh x = \frac{1}{\cosh^2 x} = \mathrm{sech}^2 x$ $\displaystyle\frac{d}{dx} \coth x = -\frac{1}{\sinh^2 x} = -\mathrm{csch}^2 x$
Inverse trigonometric functions	$\displaystyle\frac{d}{dx} \sin^{-1} x = \frac{1}{\sqrt{1 - x^2}}$ $\displaystyle\frac{d}{dx} \cos^{-1} x = -\frac{1}{\sqrt{1 - x^2}}$ $\displaystyle\frac{d}{dx} \tan^{-1} x = \frac{1}{1 + x^2}$
Inverse hyperbolic functions	$\displaystyle\frac{d}{dx} \sinh^{-1} x = \frac{1}{\sqrt{1 + x^2}}$ $\displaystyle\frac{d}{dx} \cosh^{-1} x = \frac{1}{\sqrt{x^2 - 1}}$ $\displaystyle\frac{d}{dx} \tanh^{-1} x = \frac{1}{1 - x^2}$