Lesson Plans

Lesson Seven

The Quotient Rule; Derivatives of Rational Functions

By

Michael McCallum

 

 

Introduction

 

In this lesson we introduce the quotient rule.  The rule is applied to rational functions and then to reciprocals to derive the reciprocal rule.

 

The Quotient Rule

 

 

Compare this to attempting to find the derivative by using the difference quotient.

 

Work the following examples with students working every other example, either on the board or at their desks.

 

 

Reciprocal Rule

 

Suppose y = 1/x², find the derivative.

 

We have shown that the derivative of x^-2 is –2x^-3. 

 

It can be shown that for any y = ax^-n, n ¹ 1, the derivative is –nax^-(n+1).  This is called the reciprocal rule.  This gives us another tool to calculate derivatives.  Notice that the reciprocal rule was derived using the quotient rule and applies to a special case of the quotient which we call the reciprocal.   Have the students work several examples of the reciprocal rule at the board and at their desks to complete this lesson.

 

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