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Continuity And Differentiability

Question

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$Find space dy over dx space of space straight a space straight x plus straight b space straight y squared equals cos space straight y space$

Solution

Here space space straight a space straight x plus straight b space straight y squared equals cos space straight y Didfferentiating space both space side space straight w. straight r. straight t. straight x comma space we space get comma space straight d over dx left parenthesis straight a space straight x right parenthesis plus straight d over dx left parenthesis straight b space straight y squared right parenthesis equals straight d over dx left parenthesis cos space straight y right parenthesis therefore space straight a plus 2 straight b space straight y dy over dx equals negative sin space straight y. dy over dx therefore space left parenthesis 2 straight b space straight y plus sin space straight y right parenthesis dy over dx equals negative straight a therefore dy over dx equals negative open parentheses fraction numerator straight a over denominator 2 straight b space straight y plus sin space straight y end fraction close parentheses

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