Derivative & Integral Calculator

With the central difference formula f′(x) ≈ (f(x+h) − f(x−h)) / 2h, using h = 0.00001. Sampling symmetrically around the point cancels the leading error term, making it much more accurate than a one-sided slope.

With composite Simpson's rule: the interval is split into n even subintervals, and the area is approximated by fitting a parabola through each triple of points. Doubling n roughly quarters the error — try n = 100 vs n = 1000.

Numeric methods work on any function you can type — including ones with no closed-form derivative or antiderivative — and they're accurate to about 8+ digits for smooth functions, which is plenty for checking homework.

The variable x, the operators + − * / ^ with parentheses, the functions sin, cos, tan, sqrt, cbrt, ln, log, abs, exp, and the constants pi and e. log is base-10; ln is the natural log.

The calculator detects it and says so plainly instead of returning a wrong number — for example, integrating 1/x across 0 has no finite answer, so you'll get an explanation, not NaN.