Question

$If space straight y equals square root of straight x plus square root of straight x plus square root of straight x plus......... infinity end root end root end root comma show space that space left parenthesis 2 straight y minus 1 right parenthesis dy over dx equals 1$

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Solution

Since space straight y equals square root of straight x plus square root of straight x plus square root of straight x plus......... infinity end root end root end root therefore space straight y equals square root of straight x plus straight y end root rightwards double arrow space straight y squared equals straight x plus straight y Differentiating space both space sides space straight w. straight r. straight t. straight x comma space space space space space space space space space space space space space space 2 straight y dy over dx equals 1 plus dy over dx rightwards double arrow left parenthesis 2 straight y minus 1 right parenthesis dy over dx equals 1

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