詳解：(1) 求出合成函數後再微分當 \(x \ge 0\) 時，

\(f(\sqrt x ) = {\sqrt x ^2} + 2\sqrt x  = \left| x \right| + 2\sqrt x  = x + 2\sqrt x \) \(\frac{d}{{dx}}{\rm{(}}x + 2\sqrt x {\rm{) = 1 + }}\frac{1}{{\sqrt x }}\)

(2)利用連鎖律

\(\frac{d}{{dx}}f(g(x)) = f'(g(x)) \cdot g'(x) = \left( {2\sqrt x  + 2} \right){\left( {\sqrt x } \right)^\prime } = \left( {2\sqrt x  + 2} \right)\frac{1}{{2\sqrt x }} = 1 + \frac{1}{{\sqrt x }}\)