If it is given that is differentiable at , then both pieces of the piecewise function must have the same values of and .
So let's see where the two pieces are equal to each other when :
Making that substitution, let's see where the derivatives are equal to each other at :
So, is differentiable at . You can check your work to see that this piecewise function is continuous at with these constants and that there is a single value for with these constants.