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Derivative Calculator

Find the derivative of any function of x at a given point.

Derivative Calculator Runs locally
Enter your values and press Calculate.

All calculations happen locally in your browser — nothing is uploaded, stored or tracked.

STEP 01

Type your function

Use x as the variable, e.g. x^3 − 2x + 1.

STEP 02

Choose the point

The x value where you want the derivative.

STEP 03

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

f'(x) ≈ (f(x + h) − f(x − h)) ÷ 2h
f″(x) ≈ (f(x + h) − 2f(x) + f(x − h)) ÷ h²

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).