`lim_(hrarr0) ((e+h)^(In(e+h))-e)/(h)` is-

Explanation

To solve the limit problem \( \lim_{h \to 0} \frac{(e+h)^{\ln(e+h)} - e}{h} \), we can apply the concept of differentiation using the first principle. Here’s a step-by-step solution:

### Step 1: Identify the function
Let \( f(x) = x^{\ln x} \). We want to find \( f'(e) \) using the definition of the derivative.

### Step 2: Write the definition of the derivative
The derivative of a function at a point can be defined as:
\[
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