Derivative & Integral — Symbolic d/dx, Numeric ∫
Symbolic first and second derivatives plus a numeric definite integral (Simpson’s rule). Client-side.
Use x as the variable. Supports + − * / ^, sin, cos, tan, ln, log, sqrt, exp, abs, pi, e.
Loading maths engine…
Computed with Simpson’s rule (1000 intervals).
How to use
- 1 Type a function of x, e.g. x^2, sin(x) or 1/(1+x^2).
- 2 Read its symbolic first and second derivatives instantly.
- 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 * xCommon use cases
-
1
Calculus homework
Differentiate an expression and check the result.
-
2
Definite integrals
Estimate the area under a curve between two bounds.
-
3
Analyze functions
Use first and second derivatives to find slopes and concavity.
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
- Derivative — Wolfram MathWorld — Wolfram MathWorld
- math.js — derivative() — math.js
- Simpson's rule (numeric integration) — Wikipedia
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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