Calculus › Section N · Functions of several variables › Topic N.5
The chain rule for several variables
When a quantity depends on variables that themselves depend on something else, every chain of influence contributes a rate. The multivariable chain rule multiplies along each chain and adds the results.
In this topic
- Dependencies that branch
- One independent variable
- Worked example: a chain with two links
- Worked example: a drone over terrain
- Two independent variables
- Worked example: two methods must agree
- Implicit differentiation returns
- Worked example: derivatives from an implicit curve and a sphere
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP