Chapter 7: Differentiation
The derivative as a rate of change, the rules of differentiation, and what the derivative tells you about a graph.
The chapter problem
When is the tank filling fastest?. You will model the amount in a tank as a function of time, differentiate it, and use the derivative to answer a question about the rate. By the end of the chapter the derivative is a tool you reach for, not a procedure you remember.
Where it is used: Rates, optimisation, motion, growth and any quantity that changes.
Your turn to connect it: Where would knowing how fast something is changing right now be more useful than knowing its value?
Sections
- 7.1 The derivative from first principles — tier O · refs 5.2
- 7.2 Differentiating powers and polynomials — tier O · refs 5.2
- 7.3 The product rule — tier O · refs 5.2
- 7.4 The quotient rule — tier O · refs 5.2
- 7.5 The chain rule — tier O · refs 5.2
- 7.6 The second derivative and concavity — tier O · refs 5.2
- 7.7 Rates of change in context — tier O · refs 5.2
- 7.8 Stationary points, maxima and minima — tier O · refs 5.2
- 7.9 Curve sketching — tier O · refs 5.2
- 7.10 Differentiating exponential and trigonometric functions — tier H · refs 5.2