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Continuity And Differentiability

Question

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$Find space dy over dx space where space xy squared minus straight x squared straight y equals 4$

Solution

Here space xy squared minus straight x squared space straight y equals 4 space space Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma straight x open parentheses 2 straight y dy over dx close parentheses plus straight y squared.1 minus straight x squared dy over dx minus straight y left parenthesis 2 straight x right parenthesis equals 0 therefore space 2 xy dy over dx plus straight y squared minus straight x squared dy over dx minus 2 xy equals 0 left parenthesis 2 xy minus straight x squared right parenthesis dy over dx equals 2 xy minus straight y squared therefore space space space space space space space space space space space space space dy over dx equals fraction numerator 2 xy minus straight y squared over denominator 2 xy minus straight x squared end fraction

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