Derivative calculator

Type a function and get its derivative with every step written out: which rule is used, and where. Ask for the second, third or fourth derivative, or its value at a point. Every answer is checked numerically before it is shown.

Function to differentiate

Derivative value at x =

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What can I type?

Plain text or LaTeX, or a mix. Brackets work as you'd expect, and multiplication can be left out: 2x, x sin x, (x+1)(x-2). A function takes what follows it, up to the next sign or function: sin 2x is $\sin 2x$ , and sin x cos x is $\sin x\cos x$ . The line under the box always shows how your input was read.

You type	It means
`3x^2 - 4x + 1`	$3x^2 - 4x + 1$
`x^(1/2) or sqrt(x)`	$\sqrt{x}$
`(x+1)/(x-1)`	$\frac{x+1}{x-1}$
`sin 2x`	$\sin 2x$
`sin^2 x`	$\sin^2 x$
`sin^-1 x or arcsin x`	$\arcsin x$
`sec x, cosec x, cot x`	$\sec x,\ \operatorname{cosec} x,\ \cot x$
`e^2x or e^(2x)`	$e^{2x}$
`ln\|x\|`	$\ln\|x\|$
`log_2 x`	$\log_{2} x$
`\|x - 3\|`	$\|x - 3\|$
`pi or π`	$\pi$
`\frac{x}{x+1}`	$\frac{x}{x+1}$

log on its own is base 10; use ln for the natural log. 1/2x means $\tfrac{1}{2}x$ , as on a calculator; write 1/(2x) for $\frac{1}{2x}$ .