Let $y = f\left(\frac{1}{x}\right)$ and $f'(x) = x^3$. What is the value of $\frac{dy}{dx}$ at $x = \frac{1}{2}$ ? (A) $-\frac{1}{64}$ (B) $-\frac{1}{32}$ (C) $-32$ (D) $-64$