Limits Continuity And Differentiability Question 42
Question: $ \frac{d^{n}}{dx^{n}}(logx)= $
Options:
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}} $
Show Answer
Answer:
Correct Answer: D
Solution:
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}} $
BETA
