Calculus › Section N · Functions of several variables › Topic N.6
Directional derivatives and the gradient
Partial derivatives only cover east and north. The gradient packages them into a single vector that answers every direction question at once: which way is steepest, how steep, and where does nothing change.
In this topic
- Slopes in every direction
- The gradient vector
- The directional derivative
- Worked example: one point, two rates
- Steepest ascent and descent
- Worked example: a temperature plate
- The gradient is perpendicular to level curves
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP