if ( y = sin(3x) ), then ( \frac{dy}{dx} = )\n\na ( -3cos(3x) )\nb ( -cos(3x) )\nc ( -\frac{1}{3}cos(3x)…

Explanation:

Step1: Apply the chain rule

Let (u = 3x), then (y=\sin(u)). The chain rule states that (\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}). For (y = \sin(u)), (\frac{dy}{du}=\cos(u)). For (u = 3x), (\frac{du}{dx}=3).

Step2: Substitute back

Substitute (u = 3x) and the derivatives into the chain - rule formula: (\frac{dy}{dx}=\cos(3x)\cdot3 = 3\cos(3x)).

Answer:

E. (3\cos(3x))