EXAMPLE 3 If $f(x, y) = \sin(\frac{6x}{7+y})$, calculate $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ \newline SOLUTION Using the Chain Rule for functions of one variable, we have \newline $\frac{\partial f}{\partial x} = (\Box) \cdot \frac{\partial}{\partial x}(\frac{6x}{7+y})$ \newline $= \Box$ \newline $\frac{\partial f}{\partial y} = (\Box) \cdot \frac{\partial}{\partial y}(\frac{6x}{7+y})$ \newline $= \sec(\frac{6x}{y+7})(y+7)$
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