# Rules of differentiation modules

## Overview

After completing this section, students should be able to do the following.

- Use the definition of the derivative to develop shortcut rules to find the derivatives of constants and constant multiples.
- Use the definition of the derivative to develop shortcut rules to find the derivatives of powers of xx.
- Use the definition of the derivative to develop shortcut rules to find the derivatives of sums and differences of functions.
- Compute the derivative of polynomials.
- Recognize different notation for the derivative.
- State the derivative of the natural exponential function.
- State the derivative of the sine function.

# Patterns in derivatives

## Ximera Module

Two young mathematicians think about ``short cuts'' for differentiation.

# Basic rules of differentiation

## Ximera Module

We derive the constant rule, power rule, and sum rule.

# The derivative of the natural exponential function

## Ximera Module

We derive the derivative of the natural exponential function.

# The derivative of sine

## Ximera Module

We derive the derivative of sine.