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Continuity And Differentiability

Question

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$Find space dy over dx space where space straight x squared over straight a squared plus straight y squared over straight b squared equals 2003$

Solution

Here space straight x squared over straight a squared plus straight y squared over straight b squared equals 2003 Differentiating space both space sides space straight w. straight r. straight t. space space comma we space get comma space space space fraction numerator 2 straight x over denominator straight a squared end fraction plus fraction numerator 2 straight y over denominator straight b squared end fraction dy over dx equals 0 or space space space space space fraction numerator 2 by over denominator straight b squared end fraction dy over dx equals negative fraction numerator 2 straight x over denominator straight a squared end fraction therefore space space space space dy over dx equals negative straight b squared over straight a squared straight x over straight y

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