Derivative calculator
Type a function of x, such as x^3 − 2x + sin(x), and get its derivative, simplified. Add a value of x to also see the derivative at that point and the equation of the tangent line.
Use ^ for powers, * for times (optional: 3x), sqrt, sin, cos, tan, exp, log (= ln), pi and e.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How to write functions
Use ^ for powers, * for multiplication (optional: 3x works), sqrt() for the square root and sin, cos, tan, exp, log (natural log) and pi. For example x^2 * exp(-x) or sqrt(1 + x^2).
Derivative rules
The calculator applies the same rules you learn at school: the power rule (xⁿ becomes n·xⁿ⁻¹), the product rule, the quotient rule and the chain rule. The derivative of sin(x²) is 2x·cos(x²).
Higher derivatives and tangent lines
Choose the second or third derivative for concavity or acceleration. With a value for x you get f′(x) at that point and the tangent line y = f′(a)(x − a) + f(a). Differentiation is done symbolically by math.js, in your browser. For the area under a curve, use the integral calculator.
Frequently asked questions
Is the derivative calculator free?
Yes. The derivative calculator is completely free, with no account, sign-up or usage limit.
How accurate is the result?
The tool calculates with your browser's number precision. For important calculations, always double-check what you entered.
Does it work on my phone?
Yes. The tool works in any modern browser on a phone, tablet or computer.