1. We are asked to simplify or analyze the function $$y=\frac{2x^4 \tan x}{e^{2x} \sin x}$$. 2. Recall that $$\tan x = \frac{\sin x}{\cos x}$$, so substitute this in to rewrite the function: $$y = \frac{2x^4 \cdot \frac{\sin x}{\cos x}}{e^{2x} \sin x}$$ 3. Simplify the expression by canceling $$\sin x$$ in numerator and denominator: $$y = \frac{2x^4}{e^{2x} \cos x}$$ 4. The simplified form of the function is: $$y = \frac{2x^4}{e^{2x} \cos x}$$ This shows that $$y$$ depends on $$x$$ involving polynomial, exponential, and trigonometric components. Final answer: $$y = \frac{2x^4}{e^{2x} \cos x}$$