If `f(x)=|x|^(|sinx|),` then find `f^(prime)(-pi/4)`

Explanation

To find \( f'(-\frac{\pi}{4}) \) for the function \( f(x) = |x|^{|\sin x|} \), we will follow these steps:

### Step 1: Determine the expression for \( f(x) \) around \( x = -\frac{\pi}{4} \)

Since \( x = -\frac{\pi}{4} \) is negative, we can express \( |x| \) as \( -x \). Also, we need to evaluate \( |\sin x| \) at \( x = -\frac{\pi}{4} \):

\[
\sin\left(-\frac{\pi}{4}\right) = -\frac{1}{\sqrt{2}} \quad \Rightarrow \quad |\sin\left(-\frac{\pi}{4}\right)| = \frac{1}{\sqrt{2}}
...