Derivative Calculator

Compute numerical derivatives of polynomial, trig, exponential, and log functions at any point.

Function f(x)

Point x₀

What Is the Derivative Calculator?

Computes the numerical derivative of any function at a given point using central finite differences.

f'(x) ≈ (f(x+h) − f(x−h)) / 2h

Enter f(x) using standard math notation (x^2, sin(x), exp(x), ln(x), sqrt(x), pi, e). Enter the evaluation point.

f(x) = x^2 at x = 3: f'(3) ≈ 6.0 (exact: 2x = 6).

The derivative measures the instantaneous rate of change. It is the slope of the tangent line at a point and is fundamental to all of calculus.

Use x as variable. Operators: +, -, *, /, ^. Functions: sin, cos, tan, exp, ln, log, sqrt, abs. Constants: pi, e.

Central differences with h=0.00001 give about 10 digits of accuracy for smooth functions.

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