Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Derivatives, Functions
Language:
English
Media Formats:
eBook, Interactive

# Derivatives as functions modules

## Overview

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

• Understand the derivative as a function related to the original definition of a function.
• Find the derivative function using the limit definition.
• Relate the derivative function to the derivative at a point.
• Explain the relationship between differentiability and continuity.
• Relate the graph of the function to the graph of its derivative.
• Determine whether a piecewise function is differentiable.

# Wait for the right moment

## Ximera Module

Two young mathematicians discuss derivatives as functions.

# The derivative as a function

## Ximera Module

Here we study the derivative of a function, as a function, in its own right.

# Differentiability implies continuity

## Ximera Module

We see that if a function is differentiable at a point, then it must be continuous at that point.