Numerical derivative / slope estimator

This tool estimates $f'(x_0)$ using a difference quotient. Enter a simple expression in x, a point $x_0$, and a step size $h$. Central differences are usually best for smooth functions; try smaller $h$ until the estimate stabilizes — then stop before floating-point noise dominates.

Allowed pieces: numbers, x, + - * / ^, parentheses, and sin cos tan sqrt abs log (natural) exp pi e.

Disclaimer. This is a numerical estimate, not a symbolic computer-algebra derivative. Ill-conditioned expressions, discontinuities, or tiny $h$ can produce garbage. See the site disclaimer.

Read more: What a derivative actually measures · Calculus foundations