Derivative Calculator

Differentiate functions symbolically — first, second and higher derivatives — with the rules used and a numerical verification.

Your result will appear here

Fill in the fields and press Differentiate, or pick one of the examples.

About the Derivative Calculator

Differentiates a function symbolically and simplifies the result. Set the order to 2 for the second derivative, or up to 10 for higher derivatives. Sums are differentiated term by term in the working, and the rules that the structure of your function requires (product, quotient, chain and so on) are named.

Every derivative is cross-checked against a numerical finite-difference estimate before it is displayed, so a wrong symbolic result cannot slip through silently.

Limitations

The simplified form is correct but not always the shortest possible.
Per-rule intermediate algebra inside a single term is not shown; only steps the engine can state reliably are listed.

How to use it

Type the function, e.g. x^3 * sin(x).
Set the variable and the order of the derivative.
Optionally enter a point to evaluate the derivative there, then press Differentiate.

Example

d/dx x^3

→ 3 * x^2

Formulas used

\frac{d}{dx}x^{n} = nx^{n-1}

Power rule.

(fg)' = f'g + fg',\qquad \left(\frac{f}{g}\right)' = \frac{f'g - fg'}{g^{2}}

Product and quotient rules.

\frac{d}{dx}f(g(x)) = f'(g(x))\,g'(x)

Chain rule.

Questions and answers

How do I get the second derivative?

Set “Order” to 2. The working shows the first derivative and then differentiates it again.

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About the Derivative Calculator

Limitations

How to use it

Formulas used

Questions and answers

Related tools

About the Derivative Calculator

Limitations

How to use it

Formulas used

Questions and answers