Answer
$${\frac {\partial w}{\partial x}}={\frac {\partial w}{\partial u}}*{\frac {\partial u}{\partial x}}+{\frac {\partial w}{\partial v}}*{\frac {\partial v}{\partial x}}$$
$${\frac {\partial w}{\partial y}}={\frac {\partial w}{\partial u}}*{\frac {\partial u}{\partial y}}+{\frac {\partial w}{\partial v}}*{\frac {\partial v}{\partial y}}$$
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