if y=tan^-1(x/(sqrt(1-x^2)))  then find out the value of  (dy)/(dx) 

Explanation:

Another Explanation (5): ধরি, \( x = \sin\theta \) তাহলে, \( \theta = \sin^{-1}x \) এখন, \( y = \tan^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right) \) \( y = \tan^{-1}\left(\frac{\sin\theta}{\sqrt{1-\sin^2\theta}}\right) \) \( y = \tan^{-1}\left(\frac{\sin\theta}{\sqrt{\cos^2\theta}}\right) \) \( y = \tan^{-1}\left(\frac{\sin\theta}{\cos\theta}\right) \) \( y = \tan^{-1}(\tan\theta) \) \( y = \theta \) যেহেতু \( \theta = \sin^{-1}x \), সুতরাং \( y = \sin^{-1}x \) এখন, \( \frac{dy}{dx} = \frac{d}{dx}(\sin^{-1}x) \) আমরা জানি, \( \frac{d}{dx}(\sin^{-1}x) = \frac{1}{\sqrt{1-x^2}} \) সুতরাং, \( \frac{dy}{dx} = \frac{1}{\sqrt{1-x^2}} \) 🎉