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Find dx/dy by implicit differentiation. 4 cos x sin y =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`
Posted by justaguide on February 25, 2013 at 5:42 PM (Answer #1)
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