Work through the list without notes or a calculator. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can state the product rule in symbols and in words. (Guide: “The rule”; Practice Q1)
- I can show with an example that (f · g)′ is not f′ · g′. (Guide: “Why the derivative of a product is not f′ · g′”; Practice Q6(d))
- I can explain the rule with the growing-rectangle picture, saying why the corner piece does not count. (Guide: Figure 1)
- I can explain the subtract-and-add step in the limit proof and why continuity of f is needed. (Guide: “The limit proof”)
Skills
- I can differentiate a product of a power of x with sin x, cos x, eˣ or ln x, keeping every sign. (Guide: Worked example 1; Practice Q1, Q3)
- I can use the product rule with values from a table, keeping the value f(a)g(a) separate from the slope. (Guide: Worked example 2; Practice Q2, Q6)
- I can factor a derivative such as (2x + 3)eˣ and find where the tangent line is horizontal. (Guide: Worked examples 1 and 3; Practice Q4, Q5)
- I can find the equation of a tangent line to the graph of a product. (Guide: Worked example 1; Practice Q5(c), Q7(c))
- I can differentiate a product of three factors. (Guide: “Three factors”; Practice Q7)
Reasoning
- I can decide whether a product needs the product rule, the constant multiple rule or expanding first. (Guide: “When to use it, and when not to”; Revision notes)
- I can tell a product from a composition such as sin(x²), which needs the chain rule. (Guide: “When to use it, and when not to”)
- I can justify that a horizontal tangent occurs only where a factor such as 2x + 3 is zero, because eˣ is never 0. (Practice Q5(b))
All ticked? Move on to Topic 2.9, the quotient rule, or return to the Calculus AB roadmap or the Calculus BC roadmap.