Math & Scientific
Derivative Calculator
Derivative — derivative Calculator estimates the derivative numerically with a central difference at the point you enter. This page runs that same calculation on your numbers, in your browser: no signup, no uploads, nothing stored.
Enter your expression in x and evaluate at x = and Derivative Calculator works out the derivative value with a numerical difference at the point you choose — fast, free and private, with no sign-up or uploads.
About this calculator
This form estimates a derivative at one point from nearby function values. For x^3 at x = 2, it returns approximately12. Separately, the symbolic power rule gives f′(x) = 3x² and therefore exactly12 at2; the form does not derive that symbolic expression.
How to use
- Type a function of x, for example x^2 + 3x + 2.
- Enter the point x at which you want the slope.
- Press Calculate to estimate the derivative there.
- Read the numerical estimate of f'(x), or the reason no estimate was returned at this sampling step.
Why use Derivative Calculator
Fast
Calculations run in your browser. No round trip to a server.
Private
Your inputs never leave your device. Nothing is uploaded.
Free
No signup, no paywall, no ads-in-results, no watermarks.
Accurate
Numerical estimates, with the method shown in each result.
Mobile-ready
Optimised for phones, tablets, and desktops alike.
Transparent
Honest disclaimers wherever browser limits or regional rules apply.
Common uses
Derivative in tutoring and teaching sessions
Derivative in competitive-exam practice
Use it for homework and assignment checks
Use it for verifying answers from a textbook
Use it for double-checking a spreadsheet result
Use it for quick mental-math cross-checks
Technical notes
This is a pointwise numerical check, using h = 0.000001 × max(1, |x|) and nearby function values. It compares the one-sided finite-step slopes with a heuristic tolerance before reporting their central estimate. Disagreement can result from curvature or step size, even when a derivative exists. Conversely, agreement at a finite step is not proof of differentiability. Undefined or unrepresentable function values prevent an estimate; floating-point overflow is not a mathematical domain proof. Use analytic reasoning for exact derivatives and difficult cases.
Derivative Calculator estimates the derivative numerically with a central difference at the point you enter.
Inputs are taken exactly as entered, so check for typos before trusting an answer.
All arithmetic runs in your browser using double-precision floating point, so extreme inputs may show tiny rounding differences.
FAQ
Is this a symbolic or a numerical derivative?
It is numerical. The derivative is estimated with a central-difference formula at the point you choose, not by deriving a symbolic expression.
Which functions can I use?
You can use +, minus, *, /, ^ and functions such as sin, cos, tan, exp, ln, sqrt and abs, with x as the variable.
Why is the answer slightly off from the exact value?
Finite differences have truncation and floating-point rounding errors. Their size depends on the function, input scale and chosen step; this tool does not guarantee a number of correct decimal places.
Does the Derivative Calculator send my data to a server?
No. The Derivative Calculator runs entirely in your browser, so nothing you enter is uploaded, stored, or shared.
Worked example
The derivative of f(x) = x³ is f′(x) = 3x²; at x = 2 that is 3 × 4 = 12.