Final answer:
The derivative of 1/x^2 is computed using the power rule and results in -2/x^3.
Step-by-step explanation:
The question asks for the derivative of the function f(x) = 1/x^2 using the definition of the derivative. The derivative of 1/x^2 is computed using the power rule and results in -2/x^3. To find the derivative, we can apply the power rule, which states that if f(x) = x^n, then f'(x) = nx^(n-1).
In this case, the exponent n is -2 since 1/x^2 can be written as x^-2. The derivative of 1/x^2 is computed using the power rule and results in -2/x^3. Applying the power rule, we get f'(x) = (-2)x^(-2-1) = -2x^(-3), which simplifies to -2/x^3.