What remains to be done is to check whether the derivative {{MATH_109}} exists. Start with the definition of {{MATH_110}} {{MATH_111}} Replace {{MATH_112}} with its formula, {{MATH_113}} {{MATH_114}} Note: When {{MATH_115}}, then {{MATH_116}}, but when {{MATH_117}}, then {{MATH_118}}. Therefore, instead of computing the limit above, we will compute the two one-sided limits and compare them. {{MATH_119}} {{MATH_120}} Since the two one-sided limits are not equal it follows that {{MATH_121}} Therefore, {{MATH_122}} DOES NOT EXIST, which means that {{MATH_123}} is NOT DIFFERENTIABLE at {{MATH_124}}!