Find the derivative of $f(x)=\frac{x^{2}+3^{x}}{\sqrt{x}}$ at $x=1$.

Step 1 ：Find the derivatives: \(g'(x) = 2x + 3^x \ln(3)\) and \(h'(x) = \frac{1}{2}x^{-1/2}\)

Step 2 ：Apply the quotient rule: \(f'(x) = \frac{g'(x)h(x) - g(x)h'(x)}{h(x)^2}\)

Step 3 ：Evaluate at x=1: \(f'(1) = \frac{2 + 3 \ln(3)}{1} = \boxed{3 \ln(3)}\)