d/dx {tan⁻¹ (e^x)} = কত?

Another Explanation (5): প্রশ্ন: \(\frac{d}{dx} \left( \tan^{-1} (e^x) \right)\) কত? সমাধান: ধরা যাক, \( y = \tan^{-1} (e^x) \) তাহলে, \[ \frac{dy}{dx} = \frac{1}{1 + (e^x)^2} \cdot \frac{d}{dx} (e^x) \] এখন, \(\frac{d}{dx} (e^x) = e^x\), অতএব, \[ \frac{dy}{dx} = \frac{e^x}{1 + e^{2x}} \] অতএব, \[ \boxed{\frac{d}{dx} \left( \tan^{-1} (e^x) \right) = \frac{e^x}{1 + e^{2x}}} \]