Find df/dx if f(x) =` (sin x) ^ sin x `for all `o lt x lt pi `.

Explanation

To find \( \frac{df}{dx} \) for the function \( f(x) = (\sin x)^{\sin x} \) for \( 0 < x < \pi \), we can follow these steps:

### Step 1: Rewrite the Function
Let \( y = (\sin x)^{\sin x} \).

### Step 2: Take the Natural Logarithm
Taking the natural logarithm of both sides gives:
\[
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