# If \$ u (x) \$ is harmonic and equal to \$ phi (| x |) \$, is \$ phi \$ continuously differentiable?

I was trying to show that the radial harmonic functions in the unit's ball (in $$mathbb {R} ^ n$$) are constant. For this, I suppose $$u$$ It is a radial harmonic function in the unit ball and writes.
$$u (x) = phi ( lvert x rvert)$$
for some function $$phi$$ defined in $$[01)[01)[01)[01)$$. I got stuck trying to rigorously prove that $$phi$$ It has to be differentiable.