Differentiate the following w.r.t. x:`sqrt(e^(sqrt(x))), x >0`

Explanation

To differentiate the function \( f(x) = \sqrt{e^{\sqrt{x}}} \) with respect to \( x \), we will use the chain rule and the properties of derivatives. Let's go through the steps one by one.

### Step 1: Rewrite the function
We start with the function:
\[ f(x) = \sqrt{e^{\sqrt{x}}} \]
This can be rewritten using exponent notation:
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