y'(x) = lim (delta x -> 0) (y(x + delta x) - y(x))/delta x.
y(x + delta x) = 2/(x + delta x)^2
y(x + delta x) - y(x) = 2/(x + delta x)^2 - 2/x^2 = (2 * x^2 - 2 * (x + delta x)^2)/(x^2 * (x + delta x)^2) =
= (2 * x^2 - 2 * x^2 - 4 * x * delta x - 2 * (delta x)^2)/(x^2 * (x + delta x)^2) = (- 4 * x * delta x - 2 * (delta x)^2)/(x^2 * (x + delta x)^2)
lim (delta x -> 0) (y(x + delta x) - y(x))/delta x = lim (delta x -> 0) (-4 * x - 2 * delta x)/(x^2 * (x + delta x)^2) = (-4 * x - 2 * 0)/(x^2 * (x + 0)^2) =
= -4x/x^4 = -4/x^3
Как то так.