If \( f(x)=\frac{1}{x^{2}} \), find \( f^{\prime}(2) \)

To find \( f'(2) \) for the function \( f(x) = \frac{1}{x^2} \), we first need to compute the derivative \( f'(x) \). Using the power rule, we can rewrite \( f(x) \) as \( f(x) = x^{-2} \). Taking the derivative, we have: \[ f'(x) = -2x^{-3} = -\frac{2}{x^3} \] Now, we can evaluate the derivative at \( x = 2 \): \[ f'(2) = -\frac{2}{2^3} = -\frac{2}{8} = -\frac{1}{4} \] Thus, the value of \( f'(2) \) is \(-\frac{1}{4}\).