A) \[\log x\]
B) \[{{\log }^{n}}x\]
C) \[\frac{1}{\log \,x}\]
D) 1
Correct Answer: B
Solution :
[b] \[\because \,\,\,\,\,y={{\log }^{n}}x\] On differentiating w.r.t.x, we get \[x\log x{{\log }^{2}}x{{\log }^{3}}x....{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\] \[=\frac{x\log x{{\log }^{2}}x{{\log }^{3}}x....{{\log }^{n-1}}x{{\log }^{n}}x.1}{x\log x{{\log }^{2}}x{{\log }^{3}}x....{{\log }^{n-1}}x}\] \[={{\log }^{n}}x\]
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