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**1. 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

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x - 2x^2/(sqrt(xy))