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	${\displaystyle\frac{d}{dx} \sinh^{-1} x = \frac{1}{\sqrt{1 + x^2}}}$ ${\displaystyle\frac{d}{dx} \cosh^{-1} x = \frac{1}{\sqrt{x^2 - 1}}}$ ${\displaystyle\frac{d}{dx} \tanh^{-1} x = \frac{1}{1 - x^2}}$