Question
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.)
Ask by Ortega Crawford. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\left.\frac{dy}{dx}\right|_{x=-3} = 24
\]
Solution
We start with the given function:
\[
y = 1 - 4x^2
\]
1. Compute the derivative with respect to \( x \):
\[
\frac{dy}{dx} = -8x
\]
2. Substitute \( x = -3 \) into the derivative:
\[
\left.\frac{dy}{dx}\right|_{x=-3} = -8(-3) = 24
\]
Thus, the answer is:
\[
\left.\frac{dy}{dx}\right|_{x=-3} = 24
\]
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Simplify this solution The Deep Dive
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: \[ \left.\frac{d y}{d x}\right|_{x=-3} = 24 \]
