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Varify $\large\frac{\partial^{2} y}{\partial x\partial y}=\frac{\partial^{2} y}{\partial y\partial x}$ for the following function;$\;u=\tan^{-1}\large(\frac{x}{y})$

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Toolbox:
• If $u=f(x,y)$ is the function of two independent variables then
• $\large\frac{\partial u}{\partial y (x_0,y_0)}=\frac{d}{dy}$$f(x_0,y)\;and \;\large\frac{\partial u}{\partial x(x_0,y_0)}=\large\frac{d}{dy}$$ f(x,y_0)$ Provided they exist