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MHT CET · Maths · Differentiation

For \(N \in \mathbb{N}\),
\(\frac{\mathrm{d}^{\mathrm{n}}}{\mathrm{~d} x^{\mathrm{n}}}(\log x)=\)

  1. A \(\frac{(n-1)!}{x^n}\)
  2. B \(\frac{\mathrm{n}!}{x^{\mathrm{n}}}\)
  3. C \(\frac{(\mathrm{n}-2)!}{x^{\mathrm{n}}}\)
  4. D \((-1)^{\mathrm{n}-1} \frac{(\mathrm{n}-1)!}{x^{\mathrm{n}}}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((-1)^{\mathrm{n}-1} \frac{(\mathrm{n}-1)!}{x^{\mathrm{n}}}\)

Step-by-step Solution

Detailed explanation

\(\frac{\mathrm{d}}{\mathrm{~d} x}(\log x) = \frac{1}{x} = x^{-1}\) \(\frac{\mathrm{d}^2}{\mathrm{~d} x^2}(\log x) = -x^{-2}\)