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Find dx/dy by implicit differentiation. 4 cos x sin y =1

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jesuhlocun103 | Student, College Freshman | (Level 1) Honors

Posted February 25, 2013 at 5:16 PM via web

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Find dx/dy by implicit differentiation.

4 cos x sin y =1

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 25, 2013 at 5:42 PM (Answer #1)

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It is given that `4 cos x sin y =1` . 

Take the derivative with respect to y of both the sides:

`(d(4 cos x sin y))/(dy) = (d(1))/(dy)`

=> `4*(-sin x)*(dx/dy)*sin y + 4*cos x*cos y = 0`

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

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

=> `dx/dy = cot x*cot y`

The derivative `dx/dy = cot x*cot y`

 

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chainrule | (Level 1) eNoter

Posted March 5, 2013 at 11:30 AM (Answer #3)

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4*(d/dx)[cosx*siny]=(d/dx)(1)

4[cosx*cosy*(dy/dx)-4siny*sinx]=0

4cosx*cosy*(dy/dx)-4siny*sinx=0

(dy/dx)=(siny*sinx)/(cosx*cosy)

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