wir vereinfachen mal:$$f(x)=4\left(\dfrac{\sqrt{x}}{2}+\dfrac{1}{65536}\right)=4\left(\dfrac{1}{65536}\right)+4\left(\dfrac{\sqrt{x}}{2}\right)$$
$$f'(x)=\frac{d}{dx}\left [ 4\left(\dfrac{1}{65536}\right) \right ] + \frac{d}{dx}\left [ 4\left(\dfrac{\sqrt{x}}{2}\right) \right ] = 0 + \frac{d}{dx}\left [2\sqrt{x}\right ]=\dfrac{1}{\sqrt{x}}$$