Question

$Find space dy over dx comma space where space straight y left parenthesis straight y plus 1 right parenthesis equals straight x left parenthesis straight x plus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis$

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Solution

Here space straight y left parenthesis straight y plus 1 right parenthesis equals straight x left parenthesis straight x plus 1 right parenthesis left parenthesis straight x plus 2 right parenthesis therefore space straight y squared plus straight y equals straight x cubed plus 3 straight x squared plus 2 straight x Differentiating space both space sides space straight w. straight r. straight t. space straight x comma space we space get comma space space space space space 2 straight y dy over dx plus dy over dx equals 3 straight x squared plus 6 straight x plus 2 therefore space space space space left parenthesis 2 straight y plus 1 right parenthesis dy over dx equals 3 straight x squared plus 6 straight x plus 2 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 3 straight x squared plus 6 straight x plus 2 over denominator 2 straight y plus 1 right parenthesis end fraction

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