Do you know the sufficient and necessary conditions for a function to be differentiable?
1) Use the usual rules of differentiation to find the derivative for x NOT equal to 0.
2) Use to find the derivative AT x= 0.
This problem does NOT ask if the derivative is continuous at x= 0 so it is not necessary to show that the limit of (1), as x goes to 0, is the same as (2), as I first wrote. (But you might find it interesting to do so.)