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Given the function \(y = 2x^2(2x - 1)\), we can find its derivative using the product rule. Let \(u = 2x^2\) and \(v = 2x - 1\), then \(y = uv\).

The derivative of \(u\) with respect to \(x\) is \(\frac{du}{dx} = 4x\), and the derivative of \(v\) with respect to \(x\) is \(\frac{dv}{dx} = 2\).

Using the product rule, we have \(\frac{dy}{dx} = \frac{du}{dx} \cdot v + u \cdot \frac{dv}{dx} = (4x)(2x - 1) + (2x^2)(2) = 8x^2 - 4x + 4x^2 = 12x^2 - 4x\). When \(x = -1\), \(\frac{dy}{dx} = 12(-1)^2 - 4(-1) = 16\).