use chain rule to find the derivative of the function. f(x) = sin 2x a. f(x) = 2 sin 2x b. f(x) = 2 sin x c…

Explanation:

Step1: Let $u = 2x$

Let $y=\sin u$.

Step2: Find $\frac{du}{dx}$ and $\frac{dy}{du}$

$\frac{du}{dx}=2$, $\frac{dy}{du}=\cos u$.

Step3: Apply chain - rule

The chain - rule states that $\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}$. Substitute $u = 2x$ back in. $\frac{dy}{dx}=\cos u\cdot2=2\cos 2x$.

Answer:

C. $f'(x)=2\cos 2x$