1st you need to decide if the function is continuous at x=0 (if a function is not continuous at x=0, then it can't be differentiable at x=0)

How do you decide if a piecewise function is continuous at x=0?

If f(x) is continuous at x=0, then we can look into whether or not f(x) is differentiable at x=0.

The derivative is a limit, so you need to confirm that the left hand and right hand limits of the quotient function are equal to one another. If they are, then the function is differentiable at x=0.