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Continuity And Differentiability

Question

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$Find space dy over dx where space space xy plus xe to the power of negative straight y end exponent plus ye to the power of straight x equals straight x squared$

Solution

Here space xy plus xe to the power of negative straight y end exponent plus ye to the power of straight x equals straight x squared Differentiating space both space sides space straight w. straight r. straight t. straight x comma space we space get comma space straight x dy over dx plus straight y.1 plus xe to the power of negative straight y end exponent open parentheses negative dy over dx close parentheses plus straight e to the power of negative straight y end exponent.1 plus ye to the power of straight x plus straight e to the power of straight x dy over dx equals 2 straight x therefore space open square brackets straight x minus xe to the power of negative straight y end exponent plus straight e to the power of straight x close square brackets dy over dx equals 2 straight x minus straight y minus straight e to the power of negative straight y end exponent minus ye to the power of straight x therefore space dy over dx equals fraction numerator 2 straight x minus straight y minus straight e to the power of negative straight y end exponent minus ye to the power of straight x over denominator straight x minus xe to the power of negative straight y end exponent plus straight e to the power of straight x end fraction

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