First, we use the following log laws to simplify our logarithm expression:

log ab = log a + log b

and

log aⁿ = n log a

So we can write our question as:

Next, we use the following rule (twice) to differentiate the two log terms:

For the first term,

u = sin 2x

u' = 2 cos 2x

For the second term, we put

u = x² + 1,

giving

u' = 2x

So our final answer is: