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Derivative Rules
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| | Product and Quotient Rules
This tutorial is a very thorough explanation of how to use the product rule and the quotient rule for differentiation. Both rules are carefully explained with worked-out examples. These are followed by interactive examples for students to use for practice.
 Product and Quotient Rules
The Chain Rule
This tutorial is a complete explanation of the Chain Rule for differentiation. The rule is explained and illustrated with several interactive examples. A concise table explains how the basic differentiation rules are adapted to situations where the Chain Rule is used. Links are provided to a full proof of the Chain Rule.
The Chain Rule
Implicit Differentiation
This tutorial begins with a good discussion of implicitly defined functions and their graphs. It then shows how to find the derivative of an implicitly defined function (implicit differentiation). There are six step-by-step examples, 10 drill problems on implicit differentiation, and 10 more on finding the equation of the tangent line to an implicitly defined curve. The drill problems include full solutions. This is a good page for review and practice. Unfortunately, second derivatives are not mentioned. The goals of this tutorial are to find the derivative of an implicitly defined function using implicit differentiation and to find the equation of a tangent line to a curve that implicitly defines a function.
Implicit Differentiation
Derivatives of Logarithmic and Exponential Functions
This tutorial is a complete explanation of the techniques for differentiating logarithmic and exponential functions (base e and other bases). The rules are explained and illustrated with several interactive examples. A table begun in a previous tutorial explains how these new rules are adapted to situations where the Chain Rule is used. Students learning this for the first time or who need to firm up their skills would benefit from going through this tutorial.
Derivatives of Logarithmic and Exponential Functions
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