The set of points where the function `f(x)=x|x|` is differentiable is (a) `(-oo,\ oo)` (b) `(-oo,\ 0)uu(0,\ oo)` (c) `(0,\ oo)` (d) `[0,\ oo]`

Explanation

To determine the set of points where the function \( f(x) = x|x| \) is differentiable, we will analyze the function and its derivatives.

### Step 1: Understand the function
The function \( f(x) = x|x| \) can be expressed in piecewise form:
- For \( x \geq 0 \): \( f(x) = x^2 \)
- For \( x < 0 \): \( f(x) = -x^2 \)

### Step 2: Check differentiability at critical points
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