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Continuity And Differentiability

Question

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$Find space dy over dx space where space xy equals 100 left parenthesis straight x plus straight y right parenthesis$

Solution

Here space space space space space space space space straight x space straight y equals 100 left parenthesis straight x plus straight y right parenthesis Differentiating space both space sides space straight w. straight r. straight t space. straight x space comma space we space get comma space space space space space space space space space space space straight x dy over dx plus straight y.1 equals 100 open parentheses 1 plus dy over dx close parentheses therefore space space space space space space space space space space straight x dy over dx plus straight y equals 100 plus 100 dy over dx therefore space space left parenthesis straight x minus 100 right parenthesis dy over dx equals 100 minus straight y therefore space space space space space space space space space space space space space space space space space space dy over dx equals fraction numerator 100 minus straight y over denominator straight x minus 100 end fraction

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