Logarithmic Differentiation

Differentiate the following with respect to x:

    \[\left(\ln{x}\right)^{\ln{x}}\]

Sources:

  • Hunter, J. (1972). Calculus. Glasgow: Blackie & Son. (Exercise 5, Question 1(xvi), p. 135)
  • Porter, R.I. (1963). Further Elementary Analysis (2nd ed.). London: G. Bell & Sons. (Chapter II Miscellaneous Examples, Question 27(i), p. 35)

Solution:

Use logarithmic differentiation.

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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