f(x) = 1/x
f'(x) = lim (h → 0) (1/(x + h) - 1/x)/h
f'(x) = lim (h → 0) (x/(x·(x + h)) - (x + h)/(x·(x + h)))/h
f'(x) = lim (h → 0) (x - (x + h))/(x·(x + h))/h
f'(x) = lim (h → 0) (-h)/(x·(x + h)·h)
f'(x) = lim (h → 0) -1/(x·(x + h))
f'(x) = -1/(x·x) = -1/x^2