Calculus › Section M · Vector-valued functions › Topic M.2
Differentiating and integrating vector functions
Differentiation and integration were built for numbers, yet a moving point outputs a vector. The rescue is the same one that carried limits and continuity: split the vector into components and do the ordinary calculus you already know, three times in a row.
In this topic
- The derivative, defined honestly
- Differentiate component by component
- Worked example: a tangent vector
- Higher derivatives
- Smooth curves
- Product rules, three of them
- Worked example: circular motion stays perpendicular
- Integration, component by component
- Worked example: recovering a drone's path
- Common mistakes to avoid
- Key takeaways
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Standards: 9 (BC)