$\begin{array}{l}y=3 \sin x \cos x+2 \tan x \quad x=\frac{\pi}{4} \\ y^{\prime}=\end{array}$

Step 1 ：We are given the function \(y=3 \sin x \cos x+2 \tan x\) and we are asked to find the derivative at \(x=\frac{\pi}{4}\).

Step 2 ：First, we need to find the derivative of the function. The derivative of \(\sin x\) is \(\cos x\), the derivative of \(\cos x\) is \(-\sin x\), and the derivative of \(\tan x\) is \(\sec^2 x\). We also need to use the product rule for differentiation, which states that the derivative of \(f(x)g(x)\) is \(f'(x)g(x) + f(x)g'(x)\), and the chain rule for differentiation, which states that the derivative of \(f(g(x))\) is \(f'(g(x))g'(x)\).

Step 3 ：So, the derivative of \(3 \sin x \cos x\) is \(3(\cos^2 x - \sin^2 x)\), and the derivative of \(2 \tan x\) is \(2 \sec^2 x\).

Step 4 ：Next, we substitute \(x=\frac{\pi}{4}\) into the derivative. After simplifying, we find that the derivative of the function at \(x=\frac{\pi}{4}\) is 4.

Step 5 ：Final Answer: The derivative of the function \(y=3 \sin x \cos x+2 \tan x\) at \(x=\frac{\pi}{4}\) is \(\boxed{4}\).