$ (\dfrac{\partial z}{\partial x})^2 + (\dfrac{\partial z}{\partial y})^2 \;=\; 4\sqrt{u^2+v^2} \bigg[ (\dfrac{\partial z}{\partial u})^2 + (\dfrac{\partial z}{\partial v})^2 \bigg] \ \; \ \; \ \; \ $

u$=x^2-y^2 \; \; \; ∴ \dfrac{∂u}{∂x}=2x \; \; and \; \; \dfrac{∂u}{∂y} =-2y \; \; \; …(i) \\ \; \\ \; \\ v=2xy \; \; \; ∴ \dfrac{∂v}{∂x} =2y \; \; and \; \; \dfrac{∂v}{∂y}=2x \; \; \; …(ii) \\ \; \\ \; \\ \; \\ \dfrac{\partial z}{\partial x} \;=\; …