A table of formulas for the first derivatives of common functions used in mathematics is presented.
Derivative Formulas Table
| Function \( f(x) \) | Derivative \( \dfrac{df(x)}{dx} \) |
|---|---|
| \( x^n \) | \( n x^{n-1} \) |
| \( e^x \) | \( e^x \) |
| \( \ln(x) \) | \( \dfrac{1}{x} \) |
| \( \sin x \) | \( \cos x \) |
| \( \cos x \) | \( -\sin x \) |
| \( \tan x \) | \( \sec^2(x) \) |
| \( \cot x \) | \( -\csc^2(x) \) |
| \( \sec x \) | \( \sec x \tan x \) |
| \( \csc x \) | \( -\csc x \cot x \) |
| \( \arcsin x \) | \( \dfrac{1}{\sqrt{1 - x^2}} \) |
| \( \arccos x \) | \( \dfrac{-1}{\sqrt{1 - x^2}} \) |
| \( \arctan x \) | \( \dfrac{1}{1 + x^2} \) |
| \( \sinh x \) | \( \cosh x \) |
| \( \cosh x \) | \( \sinh x \) |
| \( \tanh x \) | \( \operatorname{sech}^2(x) \) |
| \( \coth x \) | \( -\operatorname{csch}^2 x \) |
| \( \operatorname{sech} x \) | \( -\operatorname{sech} x \tanh x \) |
| \( \operatorname{csch} x \) | \( -\operatorname{csch} x \coth x \) |
| \( \operatorname{arcsinh} x \) | \( \dfrac{1}{\sqrt{x^2 + 1}} \) |
| \( \operatorname{arccosh} x \) | \( \dfrac{1}{\sqrt{x^2 - 1}} \) |
| \( \operatorname{arctanh} x \) | \( \dfrac{1}{1 - x^2} \) |