Find the value of the derivative. \( \left.\frac{d y}{d x}\right|_{x=-3} \) if \( y=1-4 x^{2} \) \( \left.\frac{d y}{d x}\right|_{x=-3}=\square \) (Simplify your answer.)

To find the derivative \( \frac{dy}{dx} \) for the given function \( y = 1 - 4x^2 \), we start by differentiating \( y \) with respect to \( x \). The derivative is: \[ \frac{dy}{dx} = -8x \] Now, we will evaluate this derivative at \( x = -3 \): \[ \left. \frac{dy}{dx} \right|_{x=-3} = -8(-3) = 24 \] Thus, the simplified answer is: \[ \left.\frac{d y}{d x}\right|_{x=-3} = 24 \]