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Continuity And Differentiability

Question

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$If space straight x space straight y plus straight y squared equals tan space straight x plus straight y comma space find dy over dx$

Solution

space space space space space space space space space space space space space space space space space straight x space straight y plus straight y squared 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 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 space straight x dy over dx plus 2 straight y dy over dx minus dy over dx equals sec squared straight x minus straight y 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 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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