Differentiate `e^(sinx)` with respect to `x` from first-principles

Explanation

To differentiate \( e^{\sin x} \) with respect to \( x \) from first principles, we will follow these steps:

### Step 1: Define the function
Let \( f(x) = e^{\sin x} \).

### Step 2: Apply the definition of the derivative
According to the first principle of differentiation, the derivative \( f'(x) \) is given by:
\[
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