Calculus › Section N · Functions of several variables › Topic N.4
Differentials in several variables
Change one input and a partial derivative tracks the effect. Change several inputs at once and their effects stack — the total differential adds them up, and it powers practical error estimates.
In this topic
- The one-variable idea, recalled
- The total differential
- Worked example: building a total differential
- Approximating a change
- Worked example: approximating a move
- What differentiability really means
- When differentiability is guaranteed
- Worked example: propagated error in a volume
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP