(Solved): The differentiable functions \( f \) and \( g \) are defined for all real numbers \( x \). Values ...

The differentiable functions \( f \) and \( g \) are defined for all real numbers \( x \). Values of \( f, f^{\prime}, g \), and \( g^{\prime} \) for various values of \( x \) are given in the table. Find each value. (a) \( \frac{d}{d x}[\sqrt{x} \cdot f(x)] \) at \( x=4 \) (b) \( \frac{d}{d x}\left[\frac{g(x)}{f(x)}\right] \) at \( x=2 \)