Define h(x)=x^3sin(1/x) for x not equal to 0 and h(0)=0. Show that h is differentiable everywhere and that h' is continuous everywhere but fails to have a derivative at one point.

I have h'(x) to be : (3 x^2) sin(1/x)-x cos(1/x) but im i don't know how to show what is being asked.