d/dx (tan sqrt(4x+3))=?

প্রশ্ন: \( \frac{d}{dx} \tan(\sqrt{4x+3}) = ? \) 🤔

সমাধান:

1. ধরি, \( u = \sqrt{4x+3} \). তাহলে, \( \frac{du}{dx} = \frac{1}{2\sqrt{4x+3}} \cdot 4 = \frac{2}{\sqrt{4x+3}} \) 🤓।
2. এখন, \( \frac{d}{dx} \tan(\sqrt{4x+3}) = \frac{d}{dx} \tan(u) \) 🧐।
3. চেইন রুল ব্যবহার করে, \( \frac{d}{dx} \tan(u) = \frac{d}{du} \tan(u) \cdot \frac{du}{dx} \) 👌।
4. আমরা জানি, \( \frac{d}{du} \tan(u) = \sec^2(u) \) 😎।
5. সুতরাং, \( \frac{d}{dx} \tan(\sqrt{4x+3}) = \sec^2(u) \cdot \frac{2}{\sqrt{4x+3}} = \frac{2}{\sqrt{4x+3}} \sec^2(\sqrt{4x+3}) \) 🎉।

অতএব, \( \frac{d}{dx} \tan(\sqrt{4x+3}) = \frac{2}{\sqrt{4x+3}} \sec^2(\sqrt{4x+3}) \) 🥳।