Numeric Derivative Calculator
Estimate a function’s slope at one point with a central difference.
How the numeric derivative calculator works
A numerical derivative estimates instantaneous slope when an analytic derivative is unavailable or when you want to check a hand calculation. This tool samples the selected function equally far to the left and right of x, subtracts those values, and divides by twice the step. The symmetric central-difference method usually cancels more first-order error than a one-sided estimate using the same step size.
The default selects x squared at x equals 3 with a step of 0.001. Sampling 2.999 and 3.001 gives nearby squared values whose difference, divided by 0.002, is 6 to floating-point precision. That matches the exact derivative 2x evaluated at 3, providing a clear verification vector for both the function selection and the central formula.
Reading numeric derivative calculator results privately
Step size is a tradeoff: a large step blurs local curvature, while an extremely tiny step can amplify floating-point cancellation. Natural log also requires both sampled points to stay above zero. The menu intentionally uses six known functions instead of evaluating arbitrary code, which keeps the page predictable and prevents pasted expressions from executing as JavaScript. This numeric derivative calculator calculation runs entirely in your browser, so the numbers you enter never leave your device.
Frequently Asked Questions
Why use a central difference instead of a forward difference?
It samples on both sides of x, which cancels the leading one-sided truncation error for smooth functions and is usually more accurate at the same step.
How should I choose the step size?
Start near 0.001 for ordinary-scale inputs, then compare nearby step sizes. A stable estimate should not swing sharply when h changes modestly.
Is the numeric derivative calculator private?
Yes. Its inputs and results stay in your browser. Bushe.co does not upload or store the values used in this calculation.
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