The derivative of sin 2x is 2cos 2x.
To find this derivative, we can apply the chain rule, which is a fundamental concept in calculus. The chain rule states that if you have a composition of functions, the derivative can be found by multiplying the derivative of the outer function by the derivative of the inner function.
In this case, the outer function is sin(u) where u = 2x. The derivative of sin(u) with respect to u is cos(u). Therefore, we have:
d/dx[sin(2x)] = cos(2x) * d/dx[2x]
Now, we need to differentiate the inner function 2x. The derivative of 2x with respect to x is simply 2. Plugging this back into our equation, we get:
d/dx[sin(2x)] = cos(2x) * 2 = 2cos(2x)
This is how we arrive at the final answer: the derivative of sin 2x is 2cos 2x.