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Find dy/dx by implicit differentiation. y cos x = 2x^2 + 4y^2

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frdsmith | Student, Grade 11 | (Level 1) eNoter

Posted March 7, 2012 at 8:08 AM via web

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Find dy/dx by implicit differentiation.

y cos x = 2x^2 + 4y^2

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 7, 2012 at 8:30 AM (Answer #1)

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The derivative `dy/dx` of y*cos x = 2x^2 + 4y^2 has to be determined.

Using implicit differentiation

`y*(-sin x) + (dy/dx)*cos x= 4x + 8y*(dy/dx)`

=> `(dy/dx)(cos x - 8y) = 4x + y*sin x`

=>` dy/dx = (4x + y*sin x)/(cos x - 8y)`

The derivative `dy/dx` of `y*cosx =2x^2 +4y^2` is `dy/dx = (4x + y*sin x)/(cos x - 8y)`

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