Question

If $y=e^{\sqrt{x}}$, then $\frac{dy}{dx}$ equals

• A. $\frac{e^x}{2\sqrt{x}}$
• B. $\frac{\sqrt{x}}{e^{\sqrt{x}}}$
• C. $\frac{x}{e^{\sqrt{x}}}$
• D. $\frac{2\sqrt{x}}{e^{\sqrt{x}}}$

Answer 1

The correct option is A

$\frac{e^x}{2\sqrt{x}}$

Explanation for the correct option:

Find the $\frac{dy}{dx}$.

Given that, $y=e^{\sqrt{x}}$
Differentiate the given equation with respect to $x$.
$\begin{array}{rcl}\frac{dy}{dx}& =& e^{\sqrt{x}}·\frac{d}{dx}\left(\sqrt{x}\right)\left[\frac{d}{dx}\left(e^x\right)=e^x\right]\\ & =& \frac{1}{2\sqrt{x}}{e}^{\sqrt{x}}\mathbf{[}\mathbf{chain}\mathbf{}\mathbf{rule}\mathbf{]}\end{array}$
Hence, option (A) is correct.