Derivative Calculator
Find the derivative of any function of x at a given point.
All calculations happen locally in your browser — nothing is uploaded, stored or tracked.
Type your function
Use x as the variable, e.g. x^3 − 2x + 1.
Choose the point
The x value where you want the derivative.
Read the result
f(x), f′(x) and f″(x) at that point.
What Is a Derivative Calculator?
The derivative of a function measures how fast it changes — its slope at a point. This calculator evaluates the first and second derivatives of any function you type, at any x value you choose, using a high-accuracy numerical method.
Type functions like x^3 − 2x + 1, sin(x), e^x or ln(x). The calculator understands the same syntax as the math calculator: +, −, *, /, ^, parentheses, and functions such as sin, cos, tan, sqrt, exp, log and ln.
How It Computes Derivatives
These are central difference formulas with an adaptively chosen step h, giving roughly 10-digit accuracy for smooth functions. The result is numerical — it does not produce a symbolic expression.
Your data never leaves your device.
Every calculation on this site runs in your browser using vanilla JavaScript. Nothing is uploaded, stored or tracked.
- 100% local, client-side calculations
- No data stored on any server
- No tracking, no analytics, no ads scripts
- Works offline once loaded
Frequently Asked Questions
What is a derivative?
It measures the instantaneous rate of change of a function — the slope of its graph at a given point.
Is this derivative exact or approximate?
It is computed numerically with a central difference formula, accurate to roughly 10 significant digits for smooth functions.
What functions can I differentiate?
Any combination of powers, polynomials, trig (sin, cos, tan), exponentials, logarithms and roots, using x as the variable.
How do I type powers?
Use the ^ symbol: x^3 means x cubed, e^(2x) means e to the power 2x.
Can I find the second derivative?
Yes — the calculator reports f″(x) alongside f′(x).