# Thread: Help with partial derivatives

1. ## Help with partial derivatives

Hello,
I need to find the stationary points and classify them

$f(x,y)=\frac{xy}{1+x^2}$

This is how I did it:

(1) $f_x(x,y)=\frac{y(1-x^2)}{(1+x^2)^2}$
(2) $f_y(x,y)=\frac{x}{1+x^2}$

(2) yields that x=0

and (1) that y=0 or x=-1, x=1

So that I have 3 stationary points. But apparently the answer is that the only stationary point is (0,0); which I could get if I insert x=0 in (1). But the problem is that I don't understand why x=-1 and x=1 aren't valid solutions.

2. Originally Posted by sebasto
Hello,
I need to find the stationary points and classify them

$f(x,y)=\frac{xy}{1+x^2}$

This is how I did it:

(1) $f_x(x,y)=\frac{y(1-x^2)}{(1+x^2)^2}$
(2) $f_y(x,y)=\frac{x}{1+x^2}$

(2) yields that x=0

and (1) that y=0 or x=-1, x=1

So that I have 3 stationary points. But apparently the answer is that the only stationary point is (0,0); which I could get if I insert x=0 in (1). But the problem is that I don't understand why x=-1 and x=1 aren't valid solutions.
Both equations have to be satisfied simultaneously. Does $x = \pm 1$ satisfy equation (2)?