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Continuity And Differentiability

Question
CBSEENMA12034898
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Differentiate the following w.r.t.x:4cosxlogex+5

Solution
Let space space space space space straight y equals 4 cos space straight x space log subscript straight e straight x plus 5 therefore space dy over dx equals straight d over dx left square bracket 4 cos space straight x space log space straight x plus 5 right square bracket equals straight d over dx left parenthesis 4 space cos space straight x space log space straight x right parenthesis plus straight d over dx left parenthesis 5 right parenthesis space space space space space space space space space space space space space equals space 4 straight d over dx left parenthesis cos space straight x space log space straight x right parenthesis plus straight d over dx left parenthesis 5 right parenthesis space space space space space space space space space space space space space equals 4 open square brackets cos space straight x. straight d over dx left parenthesis log space straight x right parenthesis. left parenthesis space straight x right parenthesis plus log space straight x. straight d over dx left parenthesis left parenthesis cos space straight x right parenthesis close square brackets plus straight d over dx left parenthesis 5 right parenthesis space space space space space space space space space space space space space equals 4 open square brackets cos space straight x.1 over straight x log space straight x. left parenthesis negative sin space straight x right parenthesis close square brackets plus 0 equals 4 open square brackets fraction numerator cos space straight x over denominator straight x end fraction minus sin space straight x. log space straight x close square brackets

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