If `y=log((1-x^2)/(1+x^2))` , then `(dy)/(dx)=` (a)`(4x^3)/(1-x^4)` (b) `-(4x)/(1-x^4)` (c) `1/(4-x^4)` (d) `-(4x^3)/(1-x^4)`

Explanation

To find the derivative of the function \( y = \log\left(\frac{1 - x^2}{1 + x^2}\right) \), we will use the chain rule and the properties of logarithms. Here’s a step-by-step solution:

### Step 1: Differentiate using the chain rule
We start by applying the chain rule to differentiate \( y \):
\[ \frac{dy}{dx} = \frac{d}{dx} \left( \log\left(\frac{1 - x^2}{1 + x^2}\right) \right) \]

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