Chain Rule Two Variables

The Multi-Variable Chain Rule: Derivatives of Compositions

Suppose that f(x,y) depends on two variables but that the x(t) and y(t) are themselves both functions of t. Then f(x(t), y(t)) is a composition of functions and the derivative of f with respect to t is computed via the multi-variable Chain Rule. In fact, this scenario is one of many different generalizations of the single variable chain rule ...

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