Answer
${dy}=\frac{1}{2\sqrt {x}}e^{\sqrt{x}}{dx}$
Work Step by Step
We evaluate the function: $y=e^{\sqrt{x}}$
$y=e^{x^{\frac{1}{2}}}$
On differentiating the above:
$\frac{dy}{dx}=e^{x^{\frac{1}{2}}}{\frac{dx^{\frac{1}{2}}}{dx}}$
or $\frac{dy}{dx}=\frac{1}{2\sqrt {x}}e^{x^{\frac{1}{2}}}$
or ${dy}=\frac{1}{2\sqrt {x}}e^{\sqrt{x}}{dx}$
The final answer is: ${dy}=\frac{1}{2\sqrt {x}}e^{\sqrt{x}}{dx}$
