Question

find the derivative of the function.
$y = -4e^{-3x^2}$
$\frac{dy}{dx} = \square$

Explanation:

Step1: Identify outer and inner functions

Let $u = -3x^2$, so $y = -4e^u$.

Step2: Apply chain rule

$\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$. $\frac{dy}{du} = -4e^u$, $\frac{du}{dx} = -6x$.

Step3: Substitute back $u$

$\frac{dy}{dx} = (-4e^{-3x^2})(-6x) = 24x e^{-3x^2}$.

Answer:

$24x e^{-3x^2}$