If\[y={{\log }^{n}}x\], where \[{{\log }^{n}}\] means log log log... (repeated n time), then \[x\,log\text{ }x\text{ }log\text{ }x\text{ }lo{{g}^{2}}x\text{ }lo{{g}^{3}}x\]\[....{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\] is equal to

If\[y={{\log }^{n}}x\], where \[{{\log }^{n}}\] means log log log... (

1.	If\[y={{\log }^{n}}x\], where \[{{\log }^{n}}\] means log log log... (repeated n time), then \[x\,log\text{ }x\text{ }log\text{ }x\text{ }lo{{g}^{2}}x\text{ }lo{{g}^{3}}x\]\[....{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\] is equal to
A.	\[\log x\]
B.	\[{{\log }^{n}}x\]
C.	\[\frac{1}{\log \,x}\]
D.	1
Answer» C. \[\frac{1}{\log \,x}\]

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If\[y={{\log }^{n}}x\], where \[{{\log }^{n}}\] means log log log... (repeated n time), then \[x\,log\text{ }x\text{ }log\text{ }x\text{ }lo{{g}^{2}}x\text{ }lo{{g}^{3}}x\]\[....{{\log }^{n-1}}x{{\log }^{n}}x\frac{dy}{dx}\] is equal to

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