To find the derivative \(\frac{dy}{dx}\) of the function \(y = (1 - 2x)^3\), we'll use the chain rule. The chain rule states that if \(y = f(u)\) and \(u = g(x)\), then \(\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}\).

Let's differentiate step by step:

Given \(y = (1 - 2x)^3\), let \(u = 1 - 2x\). Then, we have \(y = u^3\).

Now, find \(\frac{dy}{du}\):

\(\frac{dy}{du} = 3u^2\)

Next, find \(\frac{du}{dx}\):

\(\frac{du}{dx} = -2\)

Now, apply the chain rule:

\(\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = 3u^2 \cdot (-2) = -6u^2\)

Substitute back \(u = 1 - 2x\):

\(\frac{dy}{dx} = -6(1 - 2x)^2\)

Now, we can find the value of \(\frac{dy}{dx}\) at \(x = -1\):

\(\frac{dy}{dx} \bigg|_{x=-1} = -6(1 - 2(-1))^2 = -6(3)^2 = -54\)