Find the derivative of sin 2x.

To find the derivative of the function \( \sin(2x) \), we can use the chain rule from calculus. The chain rule states that if you have a composite function, the derivative can be found by multiplying the derivative of the outer function by the derivative of the inner function.

Step-by-Step Calculation

Here’s how to apply the chain rule to \( \sin(2x) \):

• Outer function: The outer function is \( \sin(u) \), where \( u = 2x \). The derivative of \( \sin(u) \) is \( \cos(u) \).
• Inner function: The inner function is \( 2x \). The derivative of \( 2x \) is \( 2 \).

Putting It All Together

Now, we combine these results:

The derivative of \( \sin(2x) \) is:

Derivative: \( \cos(2x) \cdot 2 \)

Thus, the final answer is:

Result: \( 2\cos(2x) \)