Problem 1275 (difficulty: 4/10)

For what \(\displaystyle c\) is

\(\displaystyle f(x,y)=\begin{cases} {|x|^cy \over \sqrt{x^2+y^2}} & \text{if $(x,y)\not= (0,0)$} \\ 0 & \text{if $(x,y) = (0,0)$}\end{cases}\)

differentiable?

Give me another random problem!