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

1. DLS

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2. Kelumptus

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

3. Kelumptus

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

5. DLS

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

6. DLS

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

7. DLS

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

8. DLS

9. ghazi

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

10. sirm3d

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

11. sirm3d

find the derivative by implicit differentiation

12. ghazi

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

13. DLS

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

14. sirm3d

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

15. DLS

yeah i got that,what next

16. Kelumptus

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

17. sirm3d

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

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

19. DLS

lol i know that

20. Kelumptus

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

21. ghazi

lol

22. sirm3d

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

23. ghazi

@DLS i guess you can do it now

24. DLS

what did u do with 1/y

25. sirm3d

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

26. ghazi

he differentiated it , implicitly

27. DLS

how did u get y^2

28. ghazi

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

29. sirm3d

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

30. DLS

i know that too ! :o

31. DLS

okay whats the last step?

32. sirm3d

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