Derivative Calculator
Compute the first derivative of polynomial, trigonometric, exponential and logarithmic terms.
About Derivative Calculator
Computes the first derivative f'(x) numerically using the central difference method: f'(x) ≈ [f(x+h) − f(x−h)] / (2h). Supports polynomials (x^n), trigonometric (sin, cos, tan), exponential (exp, e^x), logarithmic (ln, log), and their compositions. The step size h is chosen small enough for high accuracy on smooth functions.
Formula
Central difference
f'(x) ≈ [f(x+h) - f(x-h)] / (2h)
- f(x)
- The input function
- x
- Point of evaluation
- h
- Step size (≈1e-7)
Worked example
With the default values below, Derivative Calculator returns f'(x) of 14.99999999. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^3 + 2*x^2 - 5*x + 3
- Evaluate at x
- 2
Results
- f'(x)
- 14.99999999
- f(x)
- 9.00000000
Step by step
- 1Values used
- 2Central difference
- 3f'(x)= 14.99999999
- 4f(x)= 9.00000000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How accurate is numerical differentiation?
For smooth functions, central difference with h≈1e-7 gives about 8-10 digits of accuracy, which is sufficient for all practical purposes.
What functions are supported?
Any expression the parser handles: polynomials, sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, ln, log, sqrt, cbrt, abs, and their combinations with +, -, *, /, ^.