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Differential Calculus

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6 Sep 2010 07:16:18 IST

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e^arctan((y-x^2)/x^2) find dy/dx

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e^arctan((y-x^2)/x^2) find dy/dx

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Yagyadutt Mishra

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Joined: 19 Feb 2009

Posts: 1983

6 Sep 2010 20:25:24 IST

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I don't know why u all post the incomplete question....it feels uncomfort to solve the question.....

Bracket should be clearly mentioned ...

Ques : y = e ^ arc ( tan ( y - x ^2 ) / x ^2 )

dy / dx = e ^ arc ( tan ( y - x ^2 ) / x ^2 ) * [ differntiation of arc (.....) ] * [ differetiation of (...)]

dy / dx = y * [ x^4 / {x^4 + (y-x^2)^2}] * [ (x^2.dy/dx - 2x.y ) / x^4 ]

dy /dx = y ( x^2 .dy/dx - 2xy ) / { x^4 - (y-x^2)^2 }

Let x^4 - (y-x^2)^2 as K (for simplicity )

dy /dx = ( yx^2.dy/dx - 2xy^2 )/K

K .dy/dx = yx^2.dy/dx - 2xy^2

dy/dx ( K -yx^2) = -2xy^2

dy/dx = 2xy^2 / (yx^2 - K)

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