I was working though my problem book for Calculus and I was able to do the simple implicit differentiation questions such as:

$\displaystyle x^2$y = 1

(I don't know how to do derivatives in Latex, somebody help!)

d/dx ($\displaystyle x^2$y) = d/dx (1)

($\displaystyle x^2$)d/dx(y) + y(2x) = 0

($\displaystyle x^2$)(dy/dx) + 2xy = 0

Rearrange and you get:

dy/dx = -2y/x

So I could do that and I get the basic idea of what we're doing, but there were two questions that really stumped me.

(a) xy = tan (xy)

(b) $\displaystyle x^2$ = (arctan(y)) / (1 + $\displaystyle y^2$)

I am completely lost, any help would be muchly appreciated

EDIT: for (a) I did manage to get a line that said:

(x)(dy/dx) + y = sec(xy)

That on the right track?