Derivative calculator

Expression guide
Polynomials x^2 + 3*x x^3 - 4*x + 1
Trigonometry sin(x) cos(x) tan(x)
Logs ln(x) log(x) log10(x)
Syntax 2x + 1 sqrt(x) exp(x)

Use x as the variable, ^ for powers, pi and e for constants. ln(x) and log(x) are natural log in this calculator.

Original function -
Derivative -
Value at point -
Numeric check -
Method -
Privacy Local only
Steps

    Symbolic derivatives use Math.js loaded only on this page. If symbolic simplification is not available, the tool can estimate the derivative numerically at the selected point.

    See examples

    Polynomial derivative

    Enter x^3 - 4*x + 1 to get the derivative and evaluate it at a point.

    Trig derivative

    Use sin(x), cos(x), or tan(x) to check common calculus rules.

    Log and root functions

    Try ln(x), log(x), log10(x), sqrt(x), or exp(x) and compare symbolic and numerical results.

    About this helper

    The derivative calculator takes one function in x and differentiates it in the browser. It uses Math.js, loaded only on this helper route, to parse and simplify symbolic derivatives when possible. If a point is provided, it also evaluates the derivative there and shows a central-difference numerical check. Your formula is processed locally and is not uploaded.

    Which variable should I use?

    Use x as the variable. You can type functions such as x^2 + 3*x, sin(x), ln(x), sqrt(x), or exp(x).

    Is the result always symbolic?

    The first version uses Math.js symbolic differentiation when possible. If symbolic simplification is not available, the tool can still estimate the derivative numerically at the selected point.

    Are my functions uploaded?

    No. The function, derivative, and numerical check run locally in your browser.