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