If \( \frac{u}{x}+\frac{v}{y}=1 \) then prove that \[ \left(\frac{\partial u}{\partial x}\right)_{y}-\left(\frac{\partial v}{\pa

If \( \frac{u}{x}+\frac{v}{y}=1 \) then prove that \[ \left(\frac{\partial u}{\partial x}\right)_{y}-\left(\frac{\partial v}{\partial y}\right)_{x}=\left(\frac{x^{2}+y^{2}}{y^{2}-x^{2}}\right) \]

If \( \frac{u}{x}+\frac{v}{y}=1 \) then prove that \[ \left(\frac{\partial u}{\partial x}\right)_{y}-\left(\frac{\partial v}{\partial y}\right)_{x}=\left(\frac{x^{2}+y^{2}}{y^{2}-x^{2}}\right) \]

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