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Sponsor Area

Continuity And Differentiability

Question

$FInd space dy over dx space of space 2 straight x plus 3 straight y equals sin space straight y$

Solution

Here space 2 straight x plus 3 straight y equals sin space straight y Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma straight d over dx left parenthesis 2 straight x right parenthesis plus straight d over dx left parenthesis 3 straight y right parenthesis equals straight d over dx left parenthesis sin space straight y right parenthesis therefore space 2 plus 3 dy over dx equals cos space straight y. dy over dx therefore space left parenthesis cos space straight y minus 3 right parenthesis dy over dx equals 2 therefore space dy over dx equals fraction numerator 2 over denominator cos space straight y minus 3 end fraction