Derivatives of Common Functions
Each page explains the derivative of one function: the formula, where it comes from, a graph of the function together with its derivative, the chain rule version and worked examples you can open in the step-by-step derivative calculator. For the general rules see differentiation rules.
| Function | Derivative | |
|---|---|---|
| $\arctan x$ | $\frac{1}{1+x^2}$ | Derivative of arctan(x) → |
| $\arcsin x$ | $\frac{1}{\sqrt{1-x^2}}$ | Derivative of arcsin(x) → |
| $\arccos x$ | $-\frac{1}{\sqrt{1-x^2}}$ | Derivative of arccos(x) → |
| $\sinh x$ | $\cosh x$ | Derivative of sinh(x) → |
| $\cosh x$ | $\sinh x$ | Derivative of cosh(x) → |
| $\tanh x$ | $1-\tanh^2 x$ | Derivative of tanh(x) → |
| $\tan x$ | $\sec^2 x$ | Derivative of tan(x) → |
| $\sec x$ | $\sec x\tan x$ | Derivative of sec(x) → |
| $\cot x$ | $-\csc^2 x$ | Derivative of cot(x) → |
| $\csc x$ | $-\csc x\cot x$ | Derivative of csc(x) → |
| $\sin^2 x$ | $\sin(2x)$ | Derivative of sin²(x) → |
| $\sec^2 x$ | $2\sec^2 x\tan x$ | Derivative of sec²(x) → |
| $\frac{1}{x}$ | $-\frac{1}{x^2}$ | Derivative of 1/x → |
| $x^x$ | $x^x(\ln x + 1)$ | Derivative of x^x → |
Looking for $\ln x$, $e^x$ or $\sqrt{x}$? See the logarithm rule, the exponential rule and the root rule.