# derivatives – Is this function smooth?

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 $$f(0,0)=0$$.