Solve sin(2x)

Step-by-step solution

1. Identify the outer function $\sin(u)$ and inner function $u = 2x$.

2. The derivative of $\sin(u)$ with respect to $u$ is $\cos(u)$.

3. The derivative of the inner $2x$ with respect to $x$ is $2$.

4. Apply the chain rule: $\frac{d}{dx}\sin(2x) = \cos(2x) \cdot 2$.

5. Simplify: the result is $2\cos(2x)$.