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Derivatives of Common Functions

The derivatives you’ll meet most often. Open any row for the derivation, the reasoning and an interactive slope graph.

Derivative of ln x $\frac{d}{dx}\left[\ln\left(x\right)\right] = \frac{1}{x}$
Derivative of sin x $\frac{d}{dx}\left[\sin\left(x\right)\right] = \cos\left(x\right)$
Derivative of cos x $\frac{d}{dx}\left[\cos\left(x\right)\right] = -\sin\left(x\right)$
Derivative of tan x $\frac{d}{dx}\left[\tan\left(x\right)\right] = \sec^{2}\left(x\right)$
Derivative of eˣ $\frac{d}{dx}\left[e^{x}\right] = e^{x}$
Derivative of x² $\frac{d}{dx}\left[x^{2}\right] = 2 x$
Derivative of √x $\frac{d}{dx}\left[\sqrt{x}\right] = \frac{1}{2 \sqrt{x}}$
Derivative of 1/x $\frac{d}{dx}\left[\frac{1}{x}\right] = -\frac{1}{x^{2}}$
Derivative of sec x $\frac{d}{dx}\left[\sec\left(x\right)\right] = \sec\left(x\right) \tan\left(x\right)$
Derivative of arctan x $\frac{d}{dx}\left[\arctan\left(x\right)\right] = \frac{1}{x^{2} + 1}$
Derivative of arcsin x $\frac{d}{dx}\left[\arcsin\left(x\right)\right] = \frac{1}{\sqrt{-x^{2} + 1}}$
Derivative of x ln x $\frac{d}{dx}\left[x \ln\left(x\right)\right] = \ln\left(x\right) + 1$
Derivative of e²ˣ $\frac{d}{dx}\left[e^{2 x}\right] = 2 e^{2 x}$
Derivative of ln(2x) $\frac{d}{dx}\left[\ln\left(2 x\right)\right] = \frac{1}{x}$
Derivative of cot x $\frac{d}{dx}\left[\cot\left(x\right)\right] = -\csc^{2}\left(x\right)$

Need a function that isn’t listed? Use the derivative calculator, or see the rules behind them on derivative rules.