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DLS

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

  • one year ago
  • one year ago

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  1. DLS
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    |dw:1354339128951:dw|

    • one year ago
  2. Kelumptus
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    is that x+1/n+1/x+1/x to infinity?

    • one year ago
  3. Kelumptus
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    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...

    • one year ago
  4. DLS
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    • one year ago
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  5. DLS
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    Here's the printed question,just if its not clear

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

    • one year ago
  7. DLS
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    To prove: \[(x^{2}-y^{2}+3)\frac{dy}{dx}=1\]

    • one year ago
  8. DLS
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    @Algebraic! @ghazi @RadEn

    • one year ago
  9. ghazi
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    use this \[Y=X+\frac{ 1 }{ Y }\]

    • one year ago
  10. sirm3d
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    the given equation \[\large y=x+\frac{ 1 }{ x+\frac{ 1 }{ x+... } }\] is equivalent to \[\large y=x+\frac{ 1 }{ y }\]

    • one year ago
  11. sirm3d
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    find the derivative by implicit differentiation

    • one year ago
  12. ghazi
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    also you can substitute x at the place where you have to prove a desired result

    • one year ago
  13. DLS
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    please ellaborate,I'm doing this type of question first time

    • one year ago
  14. sirm3d
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    \[\large y = x+\frac{ 1 }{ \left[ x+\frac{ 1 }{ x+... } \right] }=x+\frac{ 1 }{ y }\] because the bracketed expression is equal to y

    • one year ago
  15. DLS
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    yeah i got that,what next

    • one year ago
  16. Kelumptus
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    Ahh, that's clever sirm3d, makes sense now. I couldn't figure this one out.

    • one year ago
  17. sirm3d
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    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 -

    • one year ago
  18. ghazi
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    LHS --- left hand side RHS--- right hand side

    • one year ago
  19. DLS
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    lol i know that

    • one year ago
  20. Kelumptus
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    Here is a good reference for implicit differentiation: http://www.intmath.com/differentiation/8-derivative-implicit-function.php

    • one year ago
  21. ghazi
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    lol

    • one year ago
  22. sirm3d
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    oops, the derivative of the RHS is \[\large 1 - \frac{ 1 }{ y^2 }(dy/dx)\]

    • one year ago
  23. ghazi
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    @DLS i guess you can do it now

    • one year ago
  24. DLS
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    what did u do with 1/y

    • one year ago
  25. sirm3d
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    \[\large \frac{ 1 }{ y }=y^{-1}\]

    • one year ago
  26. ghazi
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    he differentiated it , implicitly

    • one year ago
  27. DLS
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    how did u get y^2

    • one year ago
  28. ghazi
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    \[\frac{ dy (x^n) }{ dx }=nx^{n-1}\]

    • one year ago
  29. sirm3d
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    by power rule and chain rule, the derivative of y^(-1) is \[-1y^{-2} \frac{ dy }{ dx }\]

    • one year ago
  30. DLS
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    i know that too ! :o

    • one year ago
  31. DLS
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    okay whats the last step?

    • one year ago
  32. sirm3d
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    equate the derivative of the LHS to the derivative of the RHS, then group terms with (dy/dx)

    • one year ago
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