Calculus › Section C · Derivatives › Topic C.3
Product and quotient rules; higher derivatives
When functions multiply or divide, their derivatives do not simply multiply or divide. Two precise patterns handle it, and once differentiation is cheap, nothing stops us from differentiating twice.
In this topic
- The wrong guess, tested
- The product rule
- Worked example: a power times a trig function
- Worked example: finding where the slope flattens
- Three factors or more
- The quotient rule
- Worked example: a quotient that tidies itself
- Harvesting the rest of trigonometry
- Knowing when not to use the rule
- Higher derivatives and acceleration
- Common mistakes to avoid
- Key takeaways
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Standards: 2, 3