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AP EAMCET202023 Sep 2020Morning ShiftMathematicsDifferentiationActual

If f ( x ) = log x 2 ( log x ) , then f ' ( e ) is equal to __________

Options

  1. Ae
  2. B1 e
  3. C1 2 e
  4. D2 e

Correct answer

C. 1 2 e

Step-by-step solution

f ( x ) = log x 2 ( log x ) ⇒ f ( x ) = ln ( ln x ) ln x 2 ⇒ f ' ( x ) = ln x 2 1 x ln x - ln ( ln x ) 2 x ( 2 ln x ) 2 ⇒ f ' ( e ) = 2 e 4 = 1 2 e

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