Find the derivative of `e^(sqrt(x))` w.r.t. `x` using the first principle.

Explanation

To find the derivative of \( f(x) = e^{\sqrt{x}} \) with respect to \( x \) using the first principle of derivatives, we will follow these steps:

### Step 1: Define the function and the limit
We start with the definition of the derivative using the first principle:
\[ f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]
Here, \( f(x) = e^{\sqrt{x}} \).
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