Answer
$${\frac {\partial z}{\partial t}}={\frac {\partial z}{\partial x}}*{\frac {\partial x}{\partial t}}+{\frac {\partial z}{\partial y}}*{\frac {\partial y}{\partial t}}$$
$${\frac {\partial z}{\partial s}}={\frac {\partial z}{\partial x}}*{\frac {\partial x}{\partial s}}+{\frac {\partial z}{\partial y}}*{\frac {\partial y}{\partial s}}$$
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