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Continuity And Differentiability

Question
CBSEENMA12034912

Differentiate the following w.r.t.x:  fraction numerator sin space straight x plus log space straight x over denominator straight x to the power of 7 plus straight e to the power of straight x end fraction

Solution
Let space space space space space straight y equals fraction numerator sin space straight x plus log space straight x over denominator straight x to the power of 7 plus straight e to the power of straight x end fraction
therefore space dy over dx equals fraction numerator left parenthesis straight x to the power of 7 plus straight e to the power of straight x right parenthesis. begin display style straight d over dx end style left parenthesis sin space straight x plus log space straight x right parenthesis minus left parenthesis sin space straight x plus log space straight x right parenthesis. begin display style straight d over dx end style left parenthesis straight x to the power of 7 plus straight e to the power of straight x right parenthesis over denominator left parenthesis straight x to the power of 7 plus straight e to the power of straight x right parenthesis squared end fraction
space space space space space space space space space space space space space equals fraction numerator left parenthesis straight x to the power of 7 plus straight e to the power of straight x right parenthesis. left parenthesis cos space straight x plus begin display style 1 over straight x end style right parenthesis minus left parenthesis sin space straight x plus log space straight x right parenthesis. left parenthesis 7 straight x to the power of 6 plus straight e to the power of straight x right parenthesis over denominator left parenthesis straight x to the power of 7 plus straight e to the power of straight x right parenthesis squared end fraction

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