Find the derivative of `e^(sqrt(x))` from the first principle.

Explanation

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

### Step-by-Step Solution:

1. **Define the function**:
Let \( f(x) = e^{\sqrt{x}} \).

2. **Apply the definition of the derivative**:
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