$$\displaystyle\frac{d}{d x } \left( { 2 }^{ \sqrt{ x } } \right)$$
$\frac{\ln(2)\times 2^{\sqrt{x}}}{2\sqrt{x}}$
$\frac{\ln(2)\left(\ln(2)\sqrt{x}-1\right)\times 2^{\sqrt{x}}}{4x^{\frac{3}{2}}}$
