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 quotient rule in the correct order, including the condition that the bottom is not zero. (Guide: “The rule”; Practice Q1)
- I can explain, with an example, why the derivative of a quotient is not the quotient of the derivatives. (Guide: “Why you need a new rule”; Practice Q7(b))
- I can show where the quotient rule comes from, using the product rule. (Guide: “Where the rule comes from”; Practice Q7(a))
- I can say what swapping the two numerator terms does to the answer. (Guide: table of three features; Practice Q1, Q2)
Skills
- I can differentiate a rational function with the quotient rule and simplify the numerator. (Guide: Worked example 1; Practice Q1, Q6(a))
- I can differentiate a quotient that includes eˣ, ln x, sin x or cos x. (Guide: “When not to use the quotient rule”; Practice Q3, Q5)
- I can use values of f, f′, g and g′ from a table to find the derivative of a quotient at a point. (Guide: Worked example 2; Practice Q2, Q7(c))
- I can use the reciprocal rule, d/dx [1/g] = −g′/g². (Guide: “A special case”; Practice Q7(c))
- I can write the equation of a tangent line to the graph of a quotient. (Guide: Worked example 1; Practice Q5(c))
Reasoning
- I can decide when rewriting or simplifying first is quicker than the quotient rule. (Guide: “When not to use the quotient rule”; Practice Q4)
- I can find where the derivative of a quotient is zero by setting its numerator to zero. (Guide: Figure 1; Practice Q3, Q6(d))
- I can interpret the value and sign of the derivative of a quotient in context, with units. (Practice Q6(b), Q6(c))
All ticked? Move on to Topic 2.10, Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions, or return to the Calculus AB roadmap or the Calculus BC roadmap.