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Continuity And Differentiability

Question

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$Find space dy over straight d space where space straight x squared plus straight y squared equals 30 straight x space straight y$

Solution

Here space straight x squared plus straight y squared equals 30 straight x space straight y Differentiating space both space sides space straight w. straight r. straight t space space straight x comma space we space get comma space space space space space space space space 3 straight x squared plus 2 straight y dy over dx equals 30 straight x dy over dx plus 30 straight y.1 therefore left parenthesis 2 straight y minus 30 straight x right parenthesis dy over dx equals 30 straight y minus 3 straight x squared therefore space space space space space space space space space space space space space dy over dx equals fraction numerator 3 left parenthesis 10 straight y minus straight x squared right parenthesis over denominator 2 left parenthesis straight y minus 15 straight x right parenthesis end fraction

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