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 why d/dx [y³] is 3y² · dy/dx, using the chain rule with y as the inner function. (Guide: “The key idea”; Practice Q1)
- I can explain why an implicit dy/dx usually contains y, using two points on a curve with the same x. (Guide: Figure 1)
- I can say what a zero numerator and a zero denominator in dy/dx tell me about the tangent line. (Guide: “Horizontal and vertical tangent lines”; Practice Q3)
Skills
- I can differentiate y terms such as yⁿ, sin y, e^y and ln y with respect to x. (Guide: table in “The key idea”; Practice Q1, Q4)
- I can use the product rule on terms such as xy and x²y, keeping both terms. (Guide: Worked example 1; Practice Q2, Q5)
- I can collect the dy/dx terms, factor and divide to make dy/dx the subject. (Guide: “The method in five steps”; Practice Q5(b), Q6(a))
- I can check a point is on the curve, evaluate dy/dx with both coordinates and write the tangent line. (Guide: Worked examples 1 and 3; Practice Q5(c), Q7(b))
- I can find all points with horizontal or vertical tangents by solving with the curve’s equation. (Guide: Worked example 2; Practice Q6)
Reasoning
- I can reject a candidate point that is not on the curve, or one where the denominator of dy/dx is 0 instead of the numerator. (Guide: “Horizontal and vertical tangent lines”; Practice Q3)
- I can argue from the sign of each term that a denominator is never 0, so there is no vertical tangent. (Practice Q7(c))
- I can spot a missing dy/dx, a missing product-rule term or a constant wrongly differentiated in someone else’s work. (Guide: “Common misconceptions”; Practice Q2)
All ticked? Move on to Topic 3.3, Differentiating Inverse Functions, or return to the Calculus AB roadmap or the Calculus BC roadmap.