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 explain how the last operation in an expression decides which rule to use first. (Guide: “Step 2” and Figure 1; Practice Q2, Q3)
- I can say why (fg)′ is not f′g′ and (f/g)′ is not f′/g′. (Guide: “Common misconceptions”; Practice Q1, Q3)
- I can explain when an equation needs implicit differentiation instead of solving for y. (Guide: “Step 3”; Practice Q5(d))
- I can explain why (f⁻¹)′(b) uses f′(a), where f(a) = b, and not f′(b). (Guide: Worked example 2(c); Practice Q4)
Skills
- I can rewrite roots, reciprocals and single-term fractions as powers before differentiating. (Guide: “Step 1” and Worked example 1(a); Practice Q1, Q6(d))
- I can use log properties to simplify before differentiating. (Guide: “Step 1”; Practice Q6(b), Q7)
- I can combine the product or quotient rule with the chain rule in one calculation. (Guide: Worked example 1(b) and (c); Practice Q3, Q6(c))
- I can apply the chain rule more than once, as in sin²(3x). (Practice Q2)
- I can differentiate inverse trig functions with an inside function. (Guide: “Step 3”; Practice Q6(a))
- I can apply the chain, quotient and inverse rules to values in a table. (Guide: Worked example 2; Practice Q3)
Reasoning
- I can justify why one procedure is shorter or safer than another for a given expression. (Practice Q6(e), Q7(d))
- I can check a derivative with a second method, a value at a point or a sign check. (Guide: Worked example 1 checks; Practice Q5(d))
- I can recognise a limit of the form [f(a + h) − f(a)]/h as f′(a). (Guide: “A limit that is a derivative in disguise”)
All ticked? Move on to Topic 3.6: Calculating Higher-Order Derivatives, or return to the Calculus AB roadmap or the Calculus BC roadmap.