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

Explanation

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))`