using the tut
finding derivs
access links

derivative gateway tutorial

using the tutorial

This is a derivative tutorial module. If you are impatient, you can jump in immediately through any of the following:

by taking a practice derivative gateway test: go here, take a test, and click the links in the comments of any problems you miss.
by going through the "finding derivatives" section of this page: go down the page, and click on the explanation or example links for the derivative rules.
by using the "access link" list: which is further down the page, and expands on this list of access points to the tutorial system.

If you're not impatient, it might be worth looking first at the different parts of the tutorial. The tutorial is designed to help you learn how to take derivatives, which it does by

explaining how to find derivatives, which is what the following section does.
showing you how to find derivatives you miss when taking the practice gateway test.
linking to practice tests for each derivative rule. These links are directly accessible from the access links below, and the answers to the problems in them are also explained in the tutorial.
showing examples of specific derivative rules, which are in the following section.

Where do you go from here?

If you're unsure about how to find derivatives, go to the following section.
If you're unsure about a specific derivative rule, go to the following section and concentrate on that rule.
If you need practice with derivatives in general, take a practice test.
If you need practice with derivatives using a specific rule, go to the access links section below and take a practice test on that rule.
If you aren't sure what to do, take a practice test and pay careful attention to what you miss, why, and whether you're missing one particular type of derivative.

There are really only two parts to finding the derivative of any function: first, we must recognize the type of function, and second, we must apply the appropriate rule to find the derivative of the function. Therefore, the first line of any written out derivative solution may begin "the first thing to notice is that this is a

," and the second line may be "so we apply the rule for

What are the types of functions and rules?
The table below lists the different functions and rules we have, and gives links to explanations for them.

types of functions	example	the rule	explanation	example

compositions	sin(x^{1/ 3})	the chain rule	explanation	example
products	sin(x) (x^{1/ 3})	the product rule	explanation	example
quotients	sin(x) / (x^{1/ 3})	the quotient rule	explanation	example
sums	sin(x) + x^{1/ 3}	the rule for sums	explanation	example
constant multiples	a^{1/ 3} sin(x)	the constant multiple rule	explanation	example
basic functions	x^{1/ 3}, or sin(x)	the rule for the function	explanation

Once you know these and can recognize them, finding derivatives is a mechanical process of applying the rules in turn -- if we start with sin(x^{1/ 3}), we apply the chain rule, which then requires that we apply the rules for the derivatives of the basic functions sin(x) and x^{1/ 3}.

access links

Direct links to different parts of the tutorial system.

for general practice, or to diagnose problem areas:

to work on specific skills: take a practice test on the skill:

to see examples with specific rules: look at an example problem for:

if a specific rule doesn't make sense: see the explanation page for:

take a practice test

chain rule
const multiples
product rule
quotient rule
sum rule

UMich Deriv G/W Tutorial
Last Modified: Fri Jul 6 09:45:10 EDT 2001
Comments to glarose@umich.edu
©2001 Gavin LaRose, UM Math Dept.