d/dx{(e^(7logx))/x^6}=?

(e^(6logx))/x^6

B. 1

C. 2x²

-e^(7logx)/(6x^5)+e^(logx)/x^6

e^(4logx)/(x^6)-(logx)/x^5

সঠিক উত্তরঃ B. 1

Explanation:

Another Explanation (5):

প্রশ্ন: \(\frac{d}{dx}\left(\frac{e^{7\log x}}{x^6}\right) = ?\)

সমাধান:

আমরা জানি, \(e^{\log a} = a\)। সুতরাং, \(e^{7\log x} = e^{\log x^7} = x^7\)।

অতএব, \(\frac{e^{7\log x}}{x^6} = \frac{x^7}{x^6} = x\).

এখন, \(\frac{d}{dx}(x) = 1\).

সুতরাং, \(\frac{d}{dx}\left(\frac{e^{7\log x}}{x^6}\right) = 1\). 🎉