About the Derivative Calculator
Differentiate functions symbolically — polynomials, trig, exponential, logarithmic and chain rule — and evaluate f′(x) at a point.
Also known as: differentiation calculator, derivative solver, f prime, first derivative, second derivative, derivative of a function.
How to use this calculator
- Enter f(x), order, evaluate at x =.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
(xⁿ)′ = nxⁿ⁻¹ · (uv)′ = u′v + uv′ · (u/v)′ = (u′v − uv′)/v² · f(g(x))′ = f′(g(x))·g′(x)
Worked example
Using the values pre-filled in the calculator above:
- f(x): x^3 * sin(x) + ln(x)
- Order: First derivative f′
- Evaluate at x = = 2
the calculator returns:
- f′(x): 3x^2 · sin(x) + x^3 · cos(x) + 1 / x
- f′(2): 8.0823944295
- f(2): 7.9675265952