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Continuity And Differentiability

Question
CBSEENMA12034896

Find space dy over dx comma space when space straight y equals 3 tan space straight x plus 5 space log subscript straight a straight x plus square root of straight x minus 3 straight e to the power of straight x plus 1 over straight x.

Solution
Let space space space space straight y equals 3 tan space straight x plus 5 space log subscript straight a straight x plus square root of straight x minus 3 straight e to the power of straight x plus 1 over straight x
therefore space space space space space space straight y equals 3 tan space straight x plus 5 space log subscript straight a straight x plus straight x to the power of 1 half end exponent minus 3 straight e to the power of straight x plus straight x to the power of negative 1 end exponent
therefore space dy over dx equals 3 sec squared straight x space plus 5 log subscript straight a straight e plus 1 half straight x to the power of negative 1 half end exponent minus 3 straight e to the power of straight x minus straight x to the power of negative 2 end exponent
therefore space dy over dx equals 3 sec squared straight x plus 5 log subscript straight a straight e plus fraction numerator 1 over denominator 2 square root of straight x end fraction minus 3 straight e to the power of straight x minus 1 over straight x squared.

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