Derivative Calculator with Steps | Learn Calculus Using Limit Definition

The Limit Definition of Derivative

The derivative of a function f at a point x is defined as the limit of the difference quotient as h approaches 0:

$$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$

This calculator demonstrates the algebraic process of finding derivatives: first writing the difference quotient, simplifying it algebraically, then taking the limit as h→0.

Select a Function

Function Type:

Note: For linear and quadratic functions, the derivation will be shown with symbolic parameters (a, b, c) to demonstrate the general formula.

How to read the derivation:

We start with the limit definition of the derivative
We substitute the specific function into the difference quotient
We simplify algebraically (expand, combine like terms, factor)
We take the limit as h approaches 0
We obtain the general derivative formula

For linear and quadratic functions, parameters a, b, c are kept as symbols throughout the derivation to show the general formula.

Derivative Calculator Using the Limit Definition

The Limit Definition of Derivative

Select a Function

Algebraic Derivation