The given expression is (x^2 - 1)/x^2. To differentiate this expression with respect to x, we can use the quotient rule of differentiation. The quotient rule states that the derivative of (f(x)/g(x)) = [g(x)*f'(x) - f(x)*g'(x)]/[g(x)]^2.
Applying the quotient rule, we get:
[(x^2)*2x - (x^2 - 1)*2x]/(x^2)^2
Simplifying the expression further, we get:
[2x^3 - 2x^3 + 2x]/x^4
= 2/x^3
Therefore, the answer is option C: 4x^2 - 2 - 2/x^3.