The function `f(x)=cot^(-1)x+x` increases in the interval (a) `(1,\ oo)` (b) `(-1,\ oo)` (c) `(-oo,\ oo)` (d) `(0,\ oo)`

Explanation

To determine the intervals in which the function \( f(x) = \cot^{-1}(x) + x \) is increasing, we need to analyze the derivative of the function.

### Step 1: Find the derivative of the function
We start by differentiating \( f(x) \):
\[ f'(x) = \frac{d}{dx}(\cot^{-1}(x)) + \frac{d}{dx}(x) \]
The derivative of \( \cot^{-1}(x) \) is \( -\frac{1}{1+x^2} \) and the derivative of \( x \) is \( 1 \). Therefore, we have:
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