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Derivative Calculator

Compute the numerical derivative f ′(x) of any expression at a given point.

f ′(x) at the point
4
Numerical derivative computed with a central-difference approximation — highly accurate but not symbolic. You can use any function or constant supported by the scientific calculator (sin, cos, ln, exp, sqrt, pi, e, …); the variable must be x.

How it works

  1. 1Enter any expression in x — such as x^2, sin(x), or ln(x + 1) — using scientific-calculator syntax.
  2. 2Set the x value where you want the derivative. The tool computes f ′(x) ≈ (f(x + h) − f(x − h)) ÷ 2h with a tiny h.
  3. 3Read the result instantly. The central-difference method is highly accurate for smooth functions but is numerical, not symbolic.

Use cases

  • Checking analytical derivatives against a numerical benchmark while studying calculus.
  • Finding the slope of a curve at a specific point for physics or economics models.
  • Exploring how sensitive a formula is to changes in x without differentiating by hand.

Frequently asked questions

Is this a symbolic or numerical derivative?

Numerical. It evaluates f at two nearby points and divides by the step size, returning a number rather than a formula — accurate to several significant figures for smooth functions.

What can I use in f(x)?

Any operator or function from the scientific calculator (+, −, ×, ÷, ^, sin, cos, tan, asin, acos, atan, sqrt, cbrt, abs, exp, ln, log) plus constants pi and e. The only variable is x.

Why might the result be inaccurate at some points?

Central differences lose precision near discontinuities, vertical asymptotes, or non-differentiable points (such as abs(x) at 0 or tan(x) at π/2). Non-finite results display as —.

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