Question 1010488
f(x) = 1 / (x-1)
f'(x) = ((1/(x+h-1) - 1/(x-1)) / h
f'(x) = (x-1) - (x+h-1) / h(x-1)(x+h-1)
f'(x) = -h / h(x-1)(x+h-1)
f'(x) = -1/(x-1)(x+h-1)
limit as h--->0 f'(x) = -1 / (x-1)^2