Question

Find `dy/dx`, if `sqrt(x) + sqrt(y) = sqrt(a)`.

Answer 1

`sqrt(x) + sqrt(y) = sqrt(a)`

Differentiating both sides w.r.t. x, we get

`(1)/(2sqrt(x)) + (1)/(2sqrt(y)) * dy/dx = 0`

∴ `(1)/(2sqrt(y)) dy/dx = -(1)/(2sqrt(x))`

∴ `dy/dx = -sqrt(y/x)`.