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Continuity And Differentiability

Question
CBSEENMA12034914

Differentiate the following w.r.t.x: fraction numerator straight e to the power of straight x over denominator 1 plus cos space straight x end fraction

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

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