## DLS Group Title If "this" is true,then prove that (x^2-y^2+3)dy/dx=1 one year ago one year ago

1. DLS Group Title

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2. Kelumptus Group Title

is that x+1/n+1/x+1/x to infinity?

3. Kelumptus Group Title

I see what you mean but now that I understand the question I would have to say that I am not sure either :/. Hopefully someone more knowledgeable than myself looks at this...

4. DLS Group Title

5. DLS Group Title

Here's the printed question,just if its not clear

6. DLS Group Title

If "this" is true,then prove that (x^2-y^2+3)dy/dx=1

7. DLS Group Title

To prove: $(x^{2}-y^{2}+3)\frac{dy}{dx}=1$

8. DLS Group Title

9. ghazi Group Title

use this $Y=X+\frac{ 1 }{ Y }$

10. sirm3d Group Title

the given equation $\large y=x+\frac{ 1 }{ x+\frac{ 1 }{ x+... } }$ is equivalent to $\large y=x+\frac{ 1 }{ y }$

11. sirm3d Group Title

find the derivative by implicit differentiation

12. ghazi Group Title

also you can substitute x at the place where you have to prove a desired result

13. DLS Group Title

please ellaborate,I'm doing this type of question first time

14. sirm3d Group Title

$\large y = x+\frac{ 1 }{ \left[ x+\frac{ 1 }{ x+... } \right] }=x+\frac{ 1 }{ y }$ because the bracketed expression is equal to y

15. DLS Group Title

yeah i got that,what next

16. Kelumptus Group Title

Ahh, that's clever sirm3d, makes sense now. I couldn't figure this one out.

17. sirm3d Group Title

just take the derivative of both sides by implicit differentiation. the derivative of the LHS is $\large (dy/dx)$ the derivative of the RHS is 1 -

18. ghazi Group Title

LHS --- left hand side RHS--- right hand side

19. DLS Group Title

lol i know that

20. Kelumptus Group Title

Here is a good reference for implicit differentiation: http://www.intmath.com/differentiation/8-derivative-implicit-function.php

21. ghazi Group Title

lol

22. sirm3d Group Title

oops, the derivative of the RHS is $\large 1 - \frac{ 1 }{ y^2 }(dy/dx)$

23. ghazi Group Title

@DLS i guess you can do it now

24. DLS Group Title

what did u do with 1/y

25. sirm3d Group Title

$\large \frac{ 1 }{ y }=y^{-1}$

26. ghazi Group Title

he differentiated it , implicitly

27. DLS Group Title

how did u get y^2

28. ghazi Group Title

$\frac{ dy (x^n) }{ dx }=nx^{n-1}$

29. sirm3d Group Title

by power rule and chain rule, the derivative of y^(-1) is $-1y^{-2} \frac{ dy }{ dx }$

30. DLS Group Title

i know that too ! :o

31. DLS Group Title

okay whats the last step?

32. sirm3d Group Title

equate the derivative of the LHS to the derivative of the RHS, then group terms with (dy/dx)