Derivative and Integral Calculator: Steps, Definite Integrals and Errors

What is it?

The Derivative & Integral Calculator differentiates a function, evaluates it at a point, and works out definite integrals.

Who is it for?

Class 11–12 and college students learning calculus, and anyone checking derivatives or areas under curves.

How to use it

1. Type the function, e.g. x^3 + 2x or sin(x)*x.
2. Choose Which derivative: first, second and so on.
3. Enter a Value at x = to get the slope at that point.
4. For an integral, fill in Integrate from and to.

Typing maths

• Powers: x^2; roots: sqrt(x); multiply: 2*x or just 2x.
• Functions: sin, cos, tan, log (base 10), ln, exp, abs; constants pi and e.
• Use brackets generously: 1/(x+1) is not the same as 1/x+1.

Common errors

• Factorials (!) cannot be differentiated: use the gamma function or rewrite the expression.
• The “to” value must be bigger than the “from” value: swap them (the integral then changes sign).
• No value for …: the expression uses a letter other than x. Replace constants with numbers.

Good to know

• Trig functions use radians, as in calculus.
• Definite integrals are worked out numerically, very accurately for smooth functions. Functions with a vertical asymptote inside the range (like 1/x from −1 to 1) have no finite answer.
• Check your homework method too: teachers want the working, not just the answer.

Open the tool: Derivative & Integral Calculator

Still stuck?

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