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