We are given the function \( f(x) = (\cos x)^{\cos x} \), and we are asked to find \( \frac{d}{dx} f(0) \), i.e., the derivative of \( f(x) \) at \( x = 0 \).

### Step-by-Step Solution:

1. **Rewrite the Function**:
   The given function is in the form \( f(x) = (\cos x)^{\cos x

Learn how to find the derivative of the function f(x) = (cos x)^cos x at x = 0 with a detailed step-by-step solution. This problem involves differentiation and exponential functions, specifically applying the chain rule. Suitable for college-level mathematics.

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