A) \[\frac{(n-1)!}{{{x}^{n}}}\]
B) \[\frac{n!}{{{x}^{n}}}\]
C) \[\frac{(n-2)!}{{{x}^{n}}}\]
D) \[{{(-1)}^{n-1}}\frac{(n-1)!}{{{x}^{n}}}\]
Correct Answer: D
Solution :
[d] Let \[y=\log x\] \[\Rightarrow {{y}_{1}}=\frac{1}{x},{{y}_{2}}=\frac{-1}{{{x}^{2}}},{{y}_{3}}=\frac{2}{{{x}^{3}}},....,{{y}_{n}}=\frac{{{(-1)}^{n-1}}(n-1)!}{{{x}^{n}}}\]
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