Calculus › Section N · Functions of several variables › Topic N.3
Partial derivatives
A quantity with several inputs changes differently depending on which input you nudge. Partial derivatives measure one direction of change at a time — and they turn out to be ordinary derivatives in disguise.
In this topic
- Hold everything else still
- The definition
- Computing them: freeze and differentiate
- Worked example: first partials
- Geometry: slopes of a sliced surface
- Worked example: a cooling rod
- Three or more variables
- Second and mixed partials
- Clairaut's theorem
- Worked example: partials that need the chain rule
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP