You did not show that the function is not continuous at

, but you did show that the derivative does not exist. You mixed up the subscripts for your

's. The result when

should be

. Your function was

, not

. Also, I don't understand the notation:

. To me, that reads the derivative with respect to zero at the point

. Since zero is a constant, not a variable, I don't think that derivative is well-defined. Once you show that the limit changes as you approach

from different directions, you have sufficiently showed that the derivative does not exist at

.