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Continuity And Differentiability

Question

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

Solution

Here space 2 straight x plus 3 straight y equals sin space straight x 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 x right parenthesis therefore space 2 straight d over dx left parenthesis straight x right parenthesis plus 3 straight d over dx left parenthesis straight y right parenthesis equals straight d over dx left parenthesis sin space straight x right parenthesis therefore space 2.1 plus 3 dy over dx equals cos space straight x therefore space space space space space space space space space space space 3 dy over dx equals cos space straight x minus 2 therefore space space space space space space space space space space space space space space space dy over dx equals 1 third left parenthesis cos space straight x minus 2 right parenthesis

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