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prove a function is continuously differentiable
$f(x,y) =\begin{cases}\arctan(y/x) & x\neq 0\\ \pi/2 & x=0,y>0\\-\pi/2 & x=0,y<0.\end{cases}$
$f$ is defined on $\Bbb R^2\smallsetminus\{(0,0)\}.$
Show that $f$ is continuously differentiable on all of its domain.
Also use implicit function to show the above proof again.
Thanks!