Discuss the differentiability of `f(x)="sin"|x|`

Explanation

To determine the differentiability of the function \( f(x) = \sin |x| \), we will analyze the function at different intervals and specifically check its differentiability at the point \( x = 0 \).

### Step 1: Define the function based on the modulus
The function \( f(x) = \sin |x| \) can be expressed piecewise as:
- For \( x > 0 \): \( f(x) = \sin(x) \)
- For \( x < 0 \): \( f(x) = \sin(-x) = -\sin(x) \)

### Step 2: Check differentiability at \( x = 0 \)
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