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Derivative calculator

Differentiate any function of x with the product, quotient and chain rules, up to the third derivative, and evaluate it at a point.

  • Free
  • No sign-up
  • Works on any device

About Derivative calculator

Type a function of x and get its derivative using the power, product, quotient and chain rules, up to the third derivative. You can also evaluate the result at a point to get a slope. Good for checking calculus homework, such as d/dx of x squared times sin x.

How to use Derivative calculator

  1. Type your function of x, using ^ for powers, for example x^3*sin(x).
  2. Choose the order of the derivative, from first up to third, and optionally a point to evaluate at.
  3. Read the derivative expression and its value at that point.

Why use this tool?

Also known as

Frequently asked questions

What is the derivative of sin(x) squared?

By the chain rule it is 2 sin(x) cos(x), which also equals sin(2x). The outer power rule gives 2 sin(x), multiplied by the derivative of the inner function, cos(x).

What is the difference between the first and second derivative?

The first derivative gives the slope of the function at each point. The second derivative is the derivative of that slope, so it tells you how the slope changes, which shows whether the curve bends up or down.

Why do I need to put multiplication signs in my function?

Writing 3x or x sin(x) can be ambiguous to a parser. Typing 3*x and x*sin(x) removes any doubt, so the product and chain rules are applied the way you meant.

Is Derivative calculator free?

Yes. Derivative calculator on Toolipedia is free to use, with no sign-up and no watermark.

Is it safe to use?

Yes. Everything is worked out in your browser, and nothing you enter is sent to our server.

Does it work on my phone?

Yes. It works in any modern browser on Android and iPhone, as well as on tablets and computers. There's nothing to install.

Do I need an account?

No. Just open the page and use the tool. There's no sign-up and no email needed.

Can I put Derivative calculator on my own website?

Yes. Use the Embed on your site button under the tool to copy a short piece of code and paste it into your page. It is free, needs no account, and the tool keeps working inside your page.

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