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If sqrt(x) +sqrt(y)=4,then (dx)/(dy)at ...

If `sqrt(x)` +`sqrt(y)=4,then (dx)/(dy)at y=1.`

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We have `sqrt(x)+sqrt(y)=4`
Differentiating the given equation both sides w.r.t.x, we get
`(1)/(2sqrt(x))+(d)/(dx)(sqrt(y))=0`
`rArr(1)/(2sqrt(x))+((d)/(dy)(sqrt(y)))(dy)/(dx)=0`
`rArr(1)/(2sqrt(x))+(1)/(2sqrt(y))cdot(dy)/(dx)=0`
`rArr(dy)/(dx)=-(sqrt(y))/(sqrt(x))`
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