A) \[\frac{{{e}^{\sqrt{x}}}}{2\sqrt{x}}\]
B) \[\frac{\sqrt{x}}{{{e}^{\sqrt{x}}}}\]
C) \[\frac{x}{{{e}^{\sqrt{x}}}}\]
D) \[\frac{2\sqrt{x}}{{{e}^{\sqrt{x}}}}\]
Correct Answer: A
Solution :
\[y={{e}^{\sqrt{x}}}\]Þ \[\frac{dy}{dx}={{e}^{\sqrt{x}}}.\frac{d}{dx}\sqrt{x}\] Þ \[\frac{dy}{dx}=\frac{{{e}^{\sqrt{x}}}}{2\sqrt{x}}\].
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