QuestionFind $\frac{dy}{dx}$ for the function $y = \cos^2(3x + 2)$.

Studdy Solution
Combine the derivatives using the chain rule:
$$\frac{dy}{dx} = \frac{d}{du}(\cos(u))^2 \cdot \frac{du}{dx}$$
Substitute the derivatives from previous steps:
$$\frac{dy}{dx} = 2\cos(u)(-\sin(u)) \cdot 3$$
$$\frac{dy}{dx} = -6\cos(u)\sin(u)$$
Substitute back $u = 3x + 2$:
$$\frac{dy}{dx} = -6\cos(3x + 2)\sin(3x + 2)$$
The derivative $\frac{dy}{dx}$ is:
$$\boxed{-6\cos(3x + 2)\sin(3x + 2)}$$