Derivative of a negative power of x

First, rewrite $f(x) = \dfrac{1}{x^3}$ using a negative exponent: $f(x) = x^{-3}$. This form allows direct application of the power rule.

Apply the power rule $\frac{d}{dx}[x^n] = n x^{n-1}$ with $n = -3$: $f'(x) = -3x^{-3-1} = -3x^{-4}$. Rewriting with a positive exponent in the denominator gives $f'(x) = -\dfrac{3}{x^4}$.