# CA III.1 The Derivative of fg (The Product Rule)

**Purpose**: To develop the product rule and understand the need for it.

**Classroom Procedure**: Begin with students working in small groups on Q1 and then follow with a class discussion to establish the need for developing a rule to take the derivative of products of functions. After this students should work on investigating the rule in small groups and the practice applying it. It is a good idea to either have a whole class discussion to establish the rule or if students are in very different places to ask them to check with you before moving on to the practice portion.

**Ideas this Activity Builds On**: This activity builds on their previous investigations of derivative rules and the derivatives they are already able to find symbolically.

**Introduction/Motivation of the Activity**: The motivation for this activity is really included in Q1 - we are currently unable to find a symbolic derivative of g(x) and therefore need to develop a rule for that.

**Need to Establish by the End of Activity/Wrap-Up**: The product rule.

**Additional Notes**: In the synthesis question 3, students find d very difficult despite having completed a-c correctly. It is good for them to struggle with this however as they have to identify that the way to discover where the largest area occurs is by using the derivative.