Differentiate `cos(x^x)` with respect to `x` :

Explanation

To differentiate \( \cos(x^x) \) with respect to \( x \), we can follow these steps:

### Step 1: Identify the outer and inner functions
We have \( y = \cos(u) \) where \( u = x^x \).

### Step 2: Differentiate the outer function
Using the chain rule, the derivative of \( y \) with respect to \( u \) is:
\[
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