If `y= cot^(-1)((1+sqrt(1+x^2))/x) " then find " dy/dx`

Explanation

To find the derivative \( \frac{dy}{dx} \) for the function \( y = \cot^{-1}\left(\frac{1 + \sqrt{1 + x^2}}{x}\right) \), we can follow these steps:

### Step 1: Rewrite the Function
Let \( y = \cot^{-1}\left(\frac{1 + \sqrt{1 + x^2}}{x}\right) \).

### Step 2: Use Trigonometric Substitution
To simplify the expression, we can use the substitution \( x = \tan(\theta) \). Then, we have:
\[
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