What formula does the symbolic derivative use?

The calculator uses the formula d/dx f(x). The result and intermediate steps appear as soon as you enter the values.

Is the symbolic derivative free?

Yes, the calculator is completely free with no registration. It works online in your browser on desktop and mobile.

Symbolic derivative

Differentiate a function symbolically (2x² → 4x). Type your own function and get its derivative.

function f(x)

Supported: + − * / ^, functions sin, cos, tan, exp, ln, log, sqrt. Constants pi, e.

How symbolic differentiation works

Symbolic differentiation returns a formula for the derivative, not just a number. It differentiates according to fixed rules applied to each part of the expression. The calculator applies them automatically and simplifies the result.

Basic formulas

(xⁿ)′ = n·xⁿ⁻¹ (power)

(sin x)′ = cos x, (cos x)′ = −sin x

(eˣ)′ = eˣ, (ln x)′ = 1/x

(constant)′ = 0, (x)′ = 1

Rules

A sum is differentiated term by term, products and quotients follow special rules, and a composite function follows the chain rule. You'll find it all on the differentiation rules page.

The calculator handles polynomials, trigonometric functions, the exponential, the logarithm, and combinations of them. If you only want the value at a point, use the derivative at a point.