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![[tex]\begin{cases}x+ y = u \\y^2 = v \end{cases}[/tex]](images/latex/a8732175de9d1a3a37bc8599a589c0494d110ccb_0.png "[tex]\begin{cases}x+ y = u \\y^2 = v \end{cases}[/tex]")
![[tex]\frac {\partial f}{\partial x} = \frac {\partial f}{\partial u} \frac {\partial u}{\partial x} + \frac {\partial f}{\partial v} \frac {\partial v}{\partial x} = \frac {\partial f}{\partial u} 1 + \frac {\partial f}{\partial v} 0 = \frac {\partial f}{\partial u} [/tex]](images/latex/428c46b682d66e716d5e8b572f3a06e4d0921c92_0.png "[tex]\frac {\partial f}{\partial x} = \frac {\partial f}{\partial u} \frac {\partial u}{\partial x} + \frac {\partial f}{\partial v} \frac {\partial v}{\partial x} = \frac {\partial f}{\partial u} 1 + \frac {\partial f}{\partial v} 0 = \frac {\partial f}{\partial u} [/tex]")
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