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Derivative & Integral — Symbolic d/dx, Numeric ∫

Symbolic first and second derivatives plus a numeric definite integral (Simpson’s rule). Client-side.

Free No signup Client-side Privacy friendly Updated

Use x as the variable. Supports + − * / ^, sin, cos, tan, ln, log, sqrt, exp, abs, pi, e.

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Symbolic derivative

Definite integral (numeric)
from to

Computed with Simpson’s rule (1000 intervals).

How to use

  1. 1 Type a function of x, e.g. x^2, sin(x) or 1/(1+x^2).
  2. 2 Read its symbolic first and second derivatives instantly.
  3. 3 Set the lower and upper limits to get the definite integral numerically.

Why use this tool

  • Exact symbolic differentiation plus a fast numeric definite integral.
  • Handles trig, logs, exponentials, roots and rational functions.
  • Runs entirely in your browser — nothing is sent to a server.

Frequently asked questions

How is the derivative computed?

Symbolically — the expression is differentiated with respect to x using exact rules and then simplified, so you get a formula, not just a number.

Is the integral symbolic too?

The definite integral is computed numerically with Simpson’s rule over your chosen limits, which is accurate for smooth functions.

What functions are supported?

Arithmetic with + − * / ^, plus sin, cos, tan, asin/acos/atan, ln, log, sqrt, exp, abs, and the constants pi and e.

Why does my integral show a warning?

If the function is undefined or blows up somewhere on the interval (for example 1/x across 0), the numeric estimate diverges and a warning is shown.

What is Derivative & Integral Calculator?

A derivative and integral calculator differentiates a function of x symbolically and evaluates its definite integral numerically over a chosen interval.

Features

Symbolic derivatives

Differentiates with respect to x and simplifies, including the second derivative.

Numeric definite integral

Evaluates ∫ from a to b using composite Simpson's rule.

Free & private

Runs on your device — nothing is uploaded.

Example

Input

d/dx (x^2)

Output

2 * x

Common use cases

  1. 1

    Calculus homework

    Differentiate an expression and check the result.

  2. 2

    Definite integrals

    Estimate the area under a curve between two bounds.

  3. 3

    Analyze functions

    Use first and second derivatives to find slopes and concavity.

Summary

Zerethon's derivative & integral calculator computes symbolic derivatives (first and second) of an expression with math.js, and evaluates definite integrals numerically using Simpson's rule, in your browser. Everything runs client-side — nothing is uploaded.

Category
Math
Pricing
Free
Privacy
Browser-based
Signup
Not required

References

Privacy

Your data never leaves your browser unless explicitly stated. Derivative & Integral Calculator runs entirely client-side — no server upload, no logging, no tracking of your input.

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