I want to show that this function is smooth (i.e. $f in C^infty(mathbb{R}^2,mathbb{R})$) but I am unsure how. Is the below smooth?

$f(x,y)=left(x^{2}+y^{2}right)^{0.5}cdotleft(cosleft(10cdotcos^{-1}left(frac{x}{left(x^{2}+y^{2}right)^{0.5}}right)right)right)$

for $(x,y)neq(0,0)$ with $f(0,0)=0$.