Formulas & tables/Mathematics/Derivatives/Derivatives of elementary functions

Derivatives of elementary functions

(sin⁡x)′=cos⁡x, (cos⁡x)′=−sin⁡x, (ex)′=ex, (ln⁡x)′=1x(\sin x)'=\cos x,\ (\cos x)'=-\sin x,\ (e^x)'=e^x,\ (\ln x)'=\tfrac1x

Result unit: — (funkcje)

What it describes

Derivatives of the basic elementary functions.

Symbols

xx
variable

Where it comes from

A set of derivatives of elementary functions worth knowing by heart — sine, cosine, the exponential function, and the logarithm.

When to use it

Differentiating trigonometric, exponential, and logarithmic functions.

Example

Give the derivatives of sin⁡x\sin x and exe^x.
Substitutionbasic formulas.
Result(sin⁡x)′=cos⁡x(\sin x)'=\cos x, (ex)′=ex(e^x)'=e^x.

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