Finding Derivatives Using the Definition 

Square Root Problem 

Copyright Maplesoft, a division of Waterloo Maple Inc., 2007 

Introduction 

This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus? methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips.  Click on the buttons to watch the videos. 

 

This application is reusable. Modify the problem, then click the !!! button on the toolbar to re-execute the document to solve the new problem. 

Problem Statement 

Use the formal definition of the derivative to find the derivative of . 

Solution 

Enter the given expression in function form.

From the Expression palette, click on   .  For the placeholder,  click on from the Expression palette and fill in the given expression.

 

(3.1)

 

 

Write the difference quotent.

Type in the difference quotient using the math editor. Press [Enter].

 

(3.2)

 

 

Rationalize the numerator. Because Maple automatically simplifies to immediately, this is done in two steps.

 

First, multiple by

Copy the expression  to a new line, or use equation labels. Right-click, Expand

 

 

(3.3)

 

 

(3.4)

 

Then, divide by

 

 

(3.5)

 

 

 

 

 

Construct the limit as .

Right-click, Constructions>Limit>h, evaluate limit at 0. Or, use the expression palette, and reference the expression by its equation label ( [Ctrl][L] ).

 

(3.6)

 

Evaluate that expression to find the derivative.

Right-click, Evaluate

 

(3.7)

 

 

Legal Notice: The copyright for this application is owned by Maplesoft. The application is intended to demonstrate the use of Maple to solve a particular problem. It has been made available for product evaluation purposes only and may not be used in any other context without the express permission of Maplesoft.