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

1.	`"If "sqrt(x)+sqrt(y)=4," then find "(dy)/(dx).`
Answer» 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))`

Discussion

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