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Standard derivatives

Some functions appear so often that it pays to know their derivatives by heart: the exponential function, the natural logarithm and the trigonometric functions.

\frac{d}{dx}e^x = e^x

the exponential function

\frac{d}{dx}\ln x = \frac{1}{x}

the natural logarithm

\frac{d}{dx}\sin x = \cos x,\quad \frac{d}{dx}\cos x = -\sin x

sine and cosine

Symbols

e

Euler's number,

\approx 2.718

Example

With the chain rule: $\dfrac{d}{dx}\sin(2x) = 2\cos(2x)$ and $\dfrac{d}{dx}e^{x^2} = 2x\,e^{x^2}$ .

Don't forget to multiply by the inner derivative when the argument is not just

x

Practise differentiation for free →

← Product and chain rule · Extreme points →

Part of Calculus: Differentiation.