Implicit derivative of function, calc 3

[tnutty]

Homework Statement

Find dy/dx ;

sqrt(xy) = 1 + yx^2
or
0 = 1 + yx^2 - sqrt(xy)

Definition :

dy/dx = - F_x / F_y;

A = F_x = 2xy - 1/2 (xy)^-0.5 * y
B = F_y = x^2 - 1/2(xy)^-0.5 * x

Then dy/dx = -A / B

But the answer according to the book, is this :

4(xy)^-1.5 - y
--------------
x - 2x^2/(sqrt(xy))

 

[Dick]

They just multiplied numerator and denominator by 2*sqrt(xy).