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Continuity And Differentiability

Question
CBSEENMA12035040
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Differentiate (log x)sin x w.r.t.x.

Solution
Let space space space space space space space straight y equals left parenthesis log space straight x right parenthesis to the power of sin space straight x end exponent therefore space log space straight y equals log left parenthesis log space straight x right parenthesis to the power of sin space straight x end exponent space rightwards double arrow space log space straight y equals sin space straight x. log left parenthesis log space straight x right parenthesis to the power of sin space straight x end exponent Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space 1 over straight y dy over dx equals sin space straight x. open parentheses fraction numerator 1 over denominator log space straight x end fraction.1 over straight x close parentheses plus log left parenthesis log space straight x right parenthesis. cos space straight x rightwards double arrow space dy over dx equals straight y open square brackets fraction numerator sin space straight x over denominator straight x space log space straight x end fraction plus cos space straight x. log left parenthesis log space straight x right parenthesis close square brackets rightwards double arrow space dy over dx equals left parenthesis log space straight x right parenthesis to the power of sin space straight x end exponent open square brackets fraction numerator sin space straight x over denominator straight x space log space straight x end fraction plus cos space straight x. log left parenthesis log space straight x right parenthesis close square brackets

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