## blackrose636 2 years ago find d^2(y)/d(x^2) in terms of x and y (second derivative) 1-xy=x-y

1. VeritasVosLiberabit

$1(\frac{ dy }{ dx })-(x)\frac{ dy }{ dx}+\frac{ dx }{dx }y=\frac{ dx }{ dx }-\frac{ dy }{ dx }$ tell me how this looks it's been a while since I differentiated with this method.

2. VeritasVosLiberabit

this would be the setup to solve for the first derivative

3. mahmit2012

y=-1 & y"=0

4. Algebraic!
5. VeritasVosLiberabit

mother of god...

6. blackrose636

how did u get the second derivative? @mahmit2012

7. Algebraic!

-( x*y' + y) = 1 -y'

8. Algebraic!

solve for y'

9. Algebraic!

differentiate the expression again

10. VeritasVosLiberabit

I didn't do the second derivative yet. just do the first then repeat.

11. Algebraic!

if you get another y' in your expression for y" sub.s in your result from the first differentiation...

12. Algebraic!

Does that make sense?

13. mahmit2012

y=-1 y"=0 why you did not pay attention!

14. mahmit2012

x#1

15. blackrose636

i got y' is -y-1/x-1 then i tried doing quotient rule and thne i got confused

16. Algebraic!

you fail at math @mahmit2012

17. Algebraic!

k

18. Algebraic!

you got y' right

19. mahmit2012

every body sleeping !! cool

20. blackrose636

yeah -y-1/x-1

21. Algebraic!

now, f = ( -y-1) g = (x-1) (f/g)' = f'g -fg'/g^2 f' = -y' g' = 1 g^2 = (x-1)^2

22. Algebraic!

plug them in and use the result from the first diff. : y' = -y-1/x-1 to sub.s in for y'

23. mahmit2012

find y=-1 it's so easy !!!

24. Algebraic!

got it @blackrose636 ?

25. blackrose636

how did u even get y=-1?

26. Algebraic!

gl @Callisto

27. mahmit2012

y-xy=x-1 so y=-1 for all x#1

28. mahmit2012

@Algebraic! did you get it !

29. Callisto

Ah... 1 - xy = x-y y-xy = x-1 y (1-x) = x-1 y = (x-1) / (1-x) y=-1!

30. mahmit2012

Thank you @Callisto

31. mahmit2012

this is different seeing !