Section 2.2: The Product Rule
Key Concepts:
Note: When given a function in factored form e.g. in the form of binomial products, the Product Rule is used to
differentiate the function, instead of expanding the factors then differentiating the expanded form of the
function using the Sum and/or the Difference Rule.
differentiate the function, instead of expanding the factors then differentiating the expanded form of the
function using the Sum and/or the Difference Rule.
Lessons for Section 2.2:
The Product Rule
1. Proof of the Product Rule (a messy proof with colourful visuals)
1. Proof of the Product Rule (a messy proof with colourful visuals)
2. Another Proof of the Product Rule (a more organized proof)
3. Common Mistake When Taking a Derivative of a Product (Pay attention and don't make this common mistake!)
3. Common Mistake When Taking a Derivative of a Product (Pay attention and don't make this common mistake!)
4. The Derivatives of a Product IS NOT the Product of the Derivatives (You get warned once again!)
Applications of the Product Rule:
1. Differentiating Using the Product Rule (Example 1)
2. Differentiating Using the Product Rule (Example 2 - a challenging twist)
3. Differentiation Examples with Rational Exponents (Part 1)
4. Differentiation Examples with Rational Exponents (Part 2)
Click HERE for the option to view this YouTube video in full screen.
5. Differentiating Products of Polynomial Functions Using the Product Rule
6. Finding Derivatives and Equations of a Tangent Line Using the Product Rule
Derivatives of the Revenue, Cost and Profit Functions:
Assigned Practices:
- eBook: Read p. 89 to 93 (particularly Example 3 on p. 91)
- eBook: Do exercises on p. 93 #3 to 8, #10 to 12
- eBook: In-Class exercises p. 95 #13 to 16
