Question

what is the 2nd derivative of:
1-xy = x-y

i get (-y-1)/(x-1) for the first

the second i know is (-y-1)/(x-1)^2 but i keep getting (0)/(x-1)^2

please show me the steps i should be taking and if possible what i did wrong

Answer 1

I would solve it for y first

1-xy = x-y
y - xy = x-1
y(1 - x) = x-1
y = (x-1)/(1-x) = -1 , x ≠1

Well, isn't that special !!!

so y' = 0 and of course
y '' = 0

Wolfram took it as a pair of intersecting lines.
Notice the horizontal line y = -1
The vertical line x = 1 will give us y = any real number
e.g. (1, 4.56) will work
LS = 1 - 1(4.56)
RS = 1 - 4.56
LS = RS

http://www.wolframalpha.com/input/?i=plot+1-xy+%3D+x-y+