Calxsolver
Calculus

Derivative at a Point

Enter a function of x and a point a. The calculator estimates the derivative f'(a) with a symmetric central-difference formula, which works for any expression including trigonometric, exponential and rational functions.

Derivative at a Point

Numeric derivative of any function of x at a point.

Try:
Answerf'(1) ≈ 2.22324
  1. Functionf(x) = sin(x) * x^2
  2. Pointa = 1, f(a) = 0.841471
  3. Central differencef'(a) ≈ (f(a+h) − f(a−h)) / 2h with a small h
  4. Derivativef'(1) ≈ 2.22324
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Worked examples

Find the derivative of eˣ at x = 0 Use a numeric derivative to confirm that the derivative of the exponential at 0 is 1. Find the derivative of sin(x)·x² at x = 1 Use a numeric central-difference derivative on a product of trig and polynomial.

Key terms

Derivative The instantaneous rate of change of a function at a point.

Frequently asked questions

How accurate is the result?

The central-difference method is accurate to several significant figures for smooth functions; results are clearly marked as approximate.

What functions can I use?

Any expression in x with +, −, ×, ÷, ^ and the functions sqrt, sin, cos, tan, ln, log, exp and more.

Do I need a polynomial?

No. For polynomials you can get an exact symbolic answer from the Polynomial Derivative tool, but this works for any function.

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