72x + 5 x - ( 2x + 3 x)/(2 x)

Here's how to solve the problem:

Step 1: Identify the function and rewrite terms for easier differentiation.
The function to differentiate is:

$$y = 7^{2x} + 5 \log x - \frac{\cos(2x) + 3\tan x}{2 \sin x}$$

We assume $\log x$ refers to the natural logarithm, $\ln x$.
The third term can be split and simplified:

$$-\frac{\cos(2x) + 3\tan x}{2 \sin x} = -\frac{\cos(2x)}{2\sin x} - \frac{3\tan x}{2\sin x}$$ $$$$