Explanation: 
Another Explanation (5): ```html
\(y = \tan^{-1} \left(\frac{2x}{1-x^2}\right)\) 🤓
ধরি, \(x = \tan \theta\) 🧐
তাহলে, \(\theta = \tan^{-1} x\) 🤩
এখন, \(y = \tan^{-1} \left(\frac{2 \tan \theta}{1 - \tan^2 \theta}\right)\) 🥳
আমরা জানি, \(\frac{2 \tan \theta}{1 - \tan^2 \theta} = \tan 2\theta\) 😎
সুতরাং, \(y = \tan^{-1} (\tan 2\theta)\) 🤯
\(y = 2\theta\) 🤗
যেহেতু, \(\theta = \tan^{-1} x\), তাই \(y = 2 \tan^{-1} x\) 😈
এখন, \(x\) এর সাপেক্ষে \(y\) এর অন্তরকলন করে পাই,
\(\frac{dy}{dx} = \frac{d}{dx} (2 \tan^{-1} x)\) 😴
\(\frac{dy}{dx} = 2 \frac{d}{dx} (\tan^{-1} x)\) 🤓
আমরা জানি, \(\frac{d}{dx} (\tan^{-1} x) = \frac{1}{1+x^2}\) 😎
অতএব, \(\frac{dy}{dx} = 2 \cdot \frac{1}{1+x^2}\) 🥳
\(\frac{dy}{dx} = \frac{2}{1+x^2}\) 🎉
```
