Solve $\frac{d}{dx}\sin (2x)$

Step-by-step solution

1. Step 1 · Choose the inner function
   $$u=2x$$

   The expression is a composition, so the chain rule applies.

2. Step 2 · Chain rule
   $$\frac{d}{dx}\sin u=\cos u\cdot u^{\prime }$$

   Differentiate the outer function, then multiply by the inner derivative.

3. Step 3 · Substitute u' = 2
   $$2\cos (2x)$$

   The factor of 2 is what makes the chain rule necessary here.