Find the intervals in which the function `f(x)=log(1+x)-(2x)/(2+x)` is increasing or decreasing.

Explanation

To determine the intervals in which the function \( f(x) = \log(1+x) - \frac{2x}{2+x} \) is increasing or decreasing, we will follow these steps:

### Step 1: Find the derivative \( f'(x) \)

To find the intervals of increase or decrease, we first need to compute the derivative of the function \( f(x) \).

1. The derivative of \( \log(1+x) \) is \( \frac{1}{1+x} \).
2. The derivative of \( -\frac{2x}{2+x} \) can be found using the quotient rule. If \( u = 2x \) and \( v = 2+x \), then:
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