Table of Derivatives
Derivatives of the basic elementary functions and the differentiation rules.
Basic functions
| f(x) | f′(x) |
|---|---|
| C | 0 |
| x | 1 |
| xn | n·xn−1 |
| √x | 1 / (2√x) |
| 1/x | −1/x² |
| ex | ex |
| ax | ax·ln a |
| ln x | 1/x |
| loga x | 1 / (x·ln a) |
| sin x | cos x |
| cos x | −sin x |
| tan x | 1 / cos²x |
| cot x | −1 / sin²x |
| arcsin x | 1 / √(1 − x²) |
| arccos x | −1 / √(1 − x²) |
| arctan x | 1 / (1 + x²) |
Rules
| Function | Derivative |
|---|---|
| u + v | u′ + v′ |
| C·u | C·u′ |
| u·v | u′v + uv′ |
| u / v | (u′v − uv′) / v² |
| f(g(x)) | f′(g(x))·g′(x) |
The table gathers the derivatives studied at school. The derivative of a composite function is found with the last rule of the second table.
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