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**2. Find f'(x). Does it exist for every x? (Hint: the case when x=0 needs special attention)**

**3. What I did is, I found the derivative of x^2 sin (1/x). That is, 2xsin(1/x)-cos(1/x). Then I figured the derivative of 0 is just 0 since its a constant. So I left it that way, as a piece-wise function. It seems too easy to be true. I'm not sure if I'm doing it correctly.**