f(x)= 1/ (x-1)

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f '(x) = lim [f(x+h) - f(x)]/h = lim [1/(x+h-1) - 1/(x-1)]/h = lim [(x-1) - (x+h-1)] / [h*(x-1)*(x+h-1)] =

= lim [x-1 - x-h+1] / [h*(x-1)*(x+h-1)] = lim (-h)/ [h*(x-1)*(x+h-1)] = lim (-1)/[(x-1)*(x+h-1)] = -1/(x-1)*(x-1) = =-1/(x-1)^2

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