If `y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s` `(-2)/(1+x^2)` for all `x` (b) `(-2)/(1+x^2)` for all `|x|<1` `2/(1+x^2)` for `|x|>1` (d) none of these

Options

A. `(-2)/(1+x^(2))` for all x
B. `(-2)/(1+x^(2))" for all "|x|lt 1`
C. `(2)/(1+x^(2))" for "|x|gt1`
D. none of these

Explanation

To solve the problem, we need to differentiate the function \( y = \cos^{-1}\left(\frac{2x}{1+x^2}\right) \) with respect to \( x \). We will use the chain rule and the derivative of the inverse cosine function.

### Step-by-Step Solution:

1. **Identify the function**:
\[ y = \cos^{-1}\left(\frac{2x}{1+x^2}\right) \]
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