1. We are given two functions: $f(x) = \tan(x)$ and $g(x) = \frac{\pi}{x}$. We need to find the derivative of $f$ evaluated at $g(4)$, which is $f'(g(4))$. 2. First, evaluate $g(4)$: $$g(4) = \frac{\pi}{4}.$$ 3. Next, find $f'(x)$, the derivative of $f(x) = \tan(x)$. Recall that: $$f'(x) = \sec^2(x).$$ 4. Substitute $g(4) = \frac{\pi}{4}$ into $f'(x)$: $$f'(g(4)) = \sec^2\left(\frac{\pi}{4}\right).$$ 5. Evaluate $\sec\left(\frac{\pi}{4}\right)$: Since $\sec(x) = \frac{1}{\cos(x)}$, and $\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$, $$\sec\left(\frac{\pi}{4}\right) = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}.$$ 6. Therefore: $$f'(g(4)) = \left(\sqrt{2}\right)^2 = 2.$$ 7. The final answer is $2$, which corresponds to option (c).