Question

Find `dy/dx`, if `xsqrt(x) + ysqrt(y) = asqrt(a)`.

Answer 1

`xsqrt(x) + ysqrt(y) = asqrt(a)`

∴ `x^(3/2) + y^(3/2) = a^(3/2)`

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

`(3)/(2).x^(1/2) + (3)/(2).y^(1/2) dy/dx = 0`

∴ `(3)/(2).y^(1/2) dy/dx = -(3)/(2)x^(1/2)`

∴ `dy/dx = (-x^(1/2))/(y^(1/2)`

= `-sqrt(x/y)`