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NDA 2023 Maths · Mathematics · Derivatives · medium

If f(x)=ln x, then f'''(2) is equal to

Single correct option

If f(x)=ln⁡xf(x)=\ln x, then f′′′(2)f'''(2) is equal to
  1. A. 12\dfrac12
  2. B. −14-\dfrac14
  3. C. 18\dfrac18
  4. D. 14\dfrac14
Show answer and solution

Answer: (D) 14\dfrac14

The derivatives are f′=1xf'=\dfrac1x, f′′=−1x2f''=-\dfrac1{x^2} and the third is 2x3\dfrac2{x^3}. At x=2x=2 this is 28=14\dfrac28=\dfrac14. The value −14-\dfrac14 is f′′(2)f''(2), and 12\dfrac12 is f′(2)f'(2).
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake