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Continuity And Differentiability

Question

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$Find space dy over dx space of space straight x space straight y plus straight y squared space equals tan space straight x plus straight y$

Solution

Here space space space straight x space straight y plus straight y squared space equals tan space straight x plus straight y Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space space space space space space space straight d over dx left parenthesis straight x space straight y right parenthesis plus straight d over dy left parenthesis straight y squared right parenthesis equals straight d over dx left parenthesis tan space straight x right parenthesis plus straight d over dx left parenthesis straight y right parenthesis therefore space straight x dy over dx plus straight y.1 plus 2 straight y dy over dx equals sec squared straight x plus dy over dx therefore space left parenthesis straight x plus 2 straight y minus 1 right parenthesis dy over dx equals sec squared straight x minus straight y therefore space space space space space space space space space space space space space space space space space space space space space dy over dx equals fraction numerator sec squared straight x minus straight y over denominator straight x plus 2 straight y minus 1 end fraction

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