let f(X) = x^2 sin(1/x) for x is not equal to 0 and f(0)= 0

A) use the chain rule and the product rule to show that f is differentiable at each c is not equal to 0 and find f'(c)

B) show that f is differentiable at x = 0 and show that f(0)=0

C) show that f' is not continuous at x = 0