Calculus › Section C · Derivatives › Topic C.2
Basic differentiation rules and rates of change
The limit definition is the truth, but it is slow. A handful of rules, each proved once from that definition, turns differentiation from a three-minute puzzle into a three-second reflex.
In this topic
- Why we build rules
- Constants and the power rule
- Rewrite before you differentiate
- Sums and constant multiples
- Worked example: a tangent line from the rules
- Sine and cosine
- A preview: the natural exponential
- Worked example: mixing the rules
- Rates of change in the real world
- Worked example: the top of a throw
- Common mistakes to avoid
- Key takeaways
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Standards: 2