Use the chain rule. Add one to the power, then divide the whole bracket by (the new power times by the dericitive of whats inside the bracket)....Thus giving you (x-1)^-1/-1
If you don't want to use substitution, add one to the power to give (x−1)−1. If you then differentiate back again, you get −(x−1)−2, which is -1 times too big. We therefore need to divide what we differentiated by -1, giving the answer as −(x−1)−1.