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Find the dy/dx , x^2+y^2=sin(xy)   

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bilinmez | Student, College Freshman | eNoter

Posted May 5, 2012 at 1:19 AM via web

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Find the dy/dx ,

x^2+y^2=sin(xy)

 

 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted May 5, 2012 at 1:15 PM (Answer #1)

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You need to use implicit differentiation and chain rule such that:

`2x + 2y(dy)/(dx) = cos(xy)*(y + x*(dy)/(dx))`

You need to open the brackets such that:

`2x + 2y(dy)/(dx) = y*cos(xy) + x*cos(xy)*(dy)/(dx)`

You need to isolate the terms containing`(dy)/(dx)`  to the left such that:

`2y(dy)/(dx) -x*cos(xy)*(dy)/(dx) = y*cos(xy) - 2x`

You need to factor out `(dy)/(dx)`  such that:

`(dy)/(dx)*(2y - x*cos(xy)) = y*cos(xy) - 2x`

`(dy)/(dx) = (y*cos(xy) - 2x)/(2y - x*cos(xy))`

Hence, evaluating `(dy)/(dx)`  yields `(dy)/(dx) = (y*cos(xy) - 2x)/(2y - x*cos(xy)).`

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