The derivative of sqrte^√x with respect to x is :

The correct answer is Option (3) → $\frac{\sqrt{e^{\sqrt{x}}}}{4\sqrt{x}}$

$y=e^{\sqrt{x}/2}$

so $\frac{dy}{dx}=e^{\sqrt{x}/2}(\frac{1}{4\sqrt{x}})=\frac{\sqrt{e^{\sqrt{x}}}}{4\sqrt{x}}$