Derivative Calculator

Differentiate any function of x and see f′(x) with every rule shown — power, product, quotient, and chain rule — plus a graph of f and f′ and the slope at any point.

Derivative f′(x) —

How to Find a Derivative

Enter a function of x to see its derivative and the rules behind it.

1

Write your function of x

Type f(x) using ^ for powers, * or juxtaposition for multiplication (2x means 2·x), and function names like sin, cos, ln, exp, and sqrt — for example x^3 + 2x or sin(x)/x.

2

The calculator differentiates term by term

It applies the power, product, quotient, and chain rules, differentiates each function, and simplifies — showing every rule it used so you can follow the working, not just copy the answer.

3

Read f′(x), the graph, and the slope

The simplified derivative appears at the top, f and f′ are plotted together, and an optional point gives the exact slope there. Going the other way? The Quadratic Formula and System of Equations solvers cover algebra.

Frequently Asked Questions

How do you use this derivative calculator?
Type your function of x into the f(x) box — for example x^3 + 2x, sin(x)/x, or e^x. The calculator instantly shows the derivative f′(x) in simplified form and lists every rule it used, from the power rule to the product, quotient, and chain rules. Use ^ for powers, * or just juxtaposition for multiplication (2x means 2·x), and function names like sin, cos, tan, ln, log, exp, and sqrt.
Which differentiation rules does it show?
It applies and names the constant rule, power rule, sum and difference rules, product rule, quotient rule, and chain rule, plus the derivatives of common functions (sin, cos, tan, their inverses, ln, log, exp, sqrt, and the hyperbolic functions). For a variable raised to a variable power, such as x^x, it uses logarithmic differentiation.
Can it evaluate the derivative at a specific point?
Yes. Enter a value in the optional "Evaluate f′ at x =" field and the calculator computes the numeric value of the derivative there — that is the slope of the function at that x. Leave the field blank to see just the symbolic derivative.
What does the graph show?
The graph plots your function f(x) as a solid line and its derivative f′(x) as a dashed line on the same axes, so you can see how the slope of f matches the height of f′. Where f is rising, f′ is positive; where f has a peak or valley, f′ crosses zero.