I don\'t understand how you got that y=0 from It would seem to me that this show

Question

I don't understand how you got that y=0 from

It would seem to me that this shows that x=0 and therefore it shows nothing conclusive about y ?

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Consider y to be a constant and differentiate the given function with respect to x to find fx(x,y). fx(x,y) delta / delt x[ ln(x2 + y2+ 1)] = 1 / x2 + y2 +1 (2x) = 2x/x2+y2+1 Now, find fy(x,y) f(x,y) = delta / delta y[ ln(x2 + y2+ 1)] = 1 / x2 + y2 +1 (2x) = 2x/x2+y2+1 Since fx(x,y) = 0, we have 2x / x2+y2+1 = 0 or x = 0. Replace x with 0 in 2x/x2+y2+1 = 0 and solve for y. 2x/02+y2+1 = 0 2y = 0 y=0 Thus, we get x=0 and y = 0 Bryan Konowitz

Explanation / Answer

Ok, there is a typo in his text. When writing down the partial derivative with respect to y, the numerator contains 2y instead of 2x. Consequently, the last substituion of x=0 is into equation 2y/(x^2+y^2+1)=0 yields 2y/(0+y^2+1)=0, and from here you get y=0. Hope this helps!

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