find dy/dx of sqrt(x+y)+sqrt(xy)=6

Answer 1

Use implicit differentiation and the "chain rule".

(1/2)(x+y)^-1/2*(1 + dy/dx) + (1/2)(xy)^-1/2*[x dy/dx + y] = 0

Solve for dy/dx. You can cancel out the "1/2" factors.

(x+y)^-1/2*(1 + dy/dx) + (xy)^-1/2*[x dy/dx + y] = 0

(x+y)^-1/2*dy/dx +(xy)^-1/2*[xdy/dx]
= -(x+y)^-1/2 -(xy)^-1/2*y

Take it from there