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Continuity And Differentiability

Question
CBSEENMA12034818

Differentiate xx w.r.t.x.

Solution
space space space space space Let space straight y equals straight x to the power of straight x
therefore space log space straight y equals log space straight x to the power of straight x
therefore space log space straight y equals straight x space log space straight x
Differentiating space both space sides space straight w. straight r. straight t. space straight x comma
space space space space space 1 over straight y dy over dx equals straight x. straight d over dx left parenthesis log space straight x right parenthesis plus log space straight x. straight d over dx left parenthesis straight x right parenthesis
therefore space 1 over straight y dy over dx equals straight x.1 over straight x plus log space straight x.1 space space space space rightwards double arrow dy over dx equals straight y left square bracket 1 plus log space straight x right square bracket
therefore fraction numerator dy over denominator space space space space space space dx end fraction equals straight x to the power of straight x left square bracket 1 plus log space straight x right square bracket.

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