---
id: mat-02-derivatives
title: "Derivatives: definition and rules"
---

# Derivatives

## Derivative definition
The derivative at a point is the limit of the difference quotient.

## Derivative rules
Key rules include:
- constant and power rule
- sum and product rule
- quotient rule
- chain rule

## Derivatives of common functions
Examples:
- derivative of x^n
- derivative of sin x and cos x
- derivative of e^x and ln x

## Tangent line approximation
A derivative gives the slope of the tangent line and supports local linear approximation.

## Critical points
Critical points occur where the derivative is zero or undefined (within the domain).