Derivative Calculator
Compute the derivative of a function with respect to a variable and, if you want, its value at a specific point — right in your browser.
How is it calculated?
The derivative is computed symbolically (real differentiation rules: power, product, chain, trigonometric functions...), not by numerical approximation. If you provide a point, the symbolic result is evaluated there to get a number — for example, the derivative of x² is 2x, and at x=3 it equals 6.
Examples
Derivative of x² + 3x
The derivative of x² + 3x is 2x + 3.
Derivative of sin(x) at x = 0
The derivative of sin(x) is cos(x); at x=0 it equals 1.
Derivative using the chain rule
The derivative of (2x+1)³ is 6·(2x+1)².
Differentiation rules applied
| Rule | Example |
|---|---|
| Power | d/dx(xⁿ) = n·xⁿ⁻¹ |
| Product | d/dx(f·g) = f'·g + f·g' |
| Chain | d/dx(f(g(x))) = f'(g(x))·g'(x) |
| Trigonometric | d/dx(sin x) = cos x; d/dx(cos x) = −sin x |