Chain Rule for Partial Derivatives/Corollary 1

Theorem
Let $F = \map f {x, y}$ be a real-valued function from $\R^2$ to $\R$.

Let $x = \map X t$ and $y = \map Y t$ be real functions.

Then:
 * $F = \map F t$

and:


 * $\dfrac {\d F} {\d t} = \dfrac {\partial F} {\partial x} \dfrac {\d x} {\d t} + \dfrac {\partial F} {\partial y} \dfrac {\d Y} {\d t}$