Question regarding derivatives

Hello! I am having a lot of difficulty in terms of solving this problem, if anyone could help me that would be greatly appreciated. My teacher stated he would quiz us on this question, yet I have no clue how to approach it.

a) Set up the value of the function f(x)=xsin(1/x) at 0 to make it continuous. Then, by using the definition of the derivative, show that the new f is not differentiable at 0.

b) Determine whether the same is true for the function g(x)=x^2sin(1/x)-->after removing discontinuity at 0.

Thanks in Advance!