To find the second derivative of the function $g(x) = \sqrt{x} - \frac{1}{2}\cos x + 12\ln x$, we need to compute the first and second derivatives step by step.

First Derivative

1. Derivative of $\sqrt{x}$:

   The derivative of $\sqrt{x} = x^{1/2}$ with respect to $x$ is:

   $\frac{d}{dx}(x^{1/2}) = \frac{1}{2}x^{-\frac{1}{2}} = \frac{1}{2\sqrt{x}}$

2. Derivative of $-\frac{1}{2}\cos x$:

   The derivative of $\cos x$ is $-\sin x$, so:

   \