d^n d x^n ( x) = - Vidyadip

MCQ

${{{d^n}} \over {d{x^n}}}(\log x) =$

A
${{(n - 1)!} \over {{x^n}}}$
B
${{n\,!} \over {{x^n}}}$
C
${{(n - 2)!} \over {{x^n}}}$
✓
${( - 1)^{n - 1}}{{(n - 1)!} \over {{x^n}}}$

✓

Answer

Correct option: D.

${( - 1)^{n - 1}}{{(n - 1)!} \over {{x^n}}}$

d
(d) Let $y = \log x$

==>${y_1} = \frac{1}{x}$, ${y_2} = \frac{{ - 1}}{{{x^2}}}$, ${y_3} = \frac{2}{{{x^3}}}$,……${y_n} = \frac{{{{( - 1)}^{n - 1}}(n - 1)!}}{{{x^n}}}$.

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