If sqrt(x/y)+sqrt(y/x)=6, find dy/dx?
Try implicit fifferentiation. Differentiate both sides of the equation with respect to x, treating y as a function of x. You do NOT have to solve for the y(x) function first.
(1/2)(x/y)^(-1/2)* d(x/y)/dx
+ (1/2)(y/x)^(-1/2)* d(y/x)/dx = 0
d(x/y)/dx = - y/x
(1/y)- (x/y^2)(dy/dx) = y/x
Solve for dy/dx as a function of x and y. Given a value of x, use the original equation to solve for y, and then use both x and y to solve for dy/dx.