Problem 1297 (difficulty: 4/10)

Is the function

\(\displaystyle f(x,y,z)=\begin{cases} \frac{\sin^2x+\sin^2y+\sin^2z}{x^2+y^2+z^2} & (x,y,z)\ne(0,0,0) \\ 1 & x=y=z=0 \\ \end{cases} \)

differentiable at the origin?

Give me another random problem!