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DLS

  • 3 years ago

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

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  1. DLS
    • 3 years ago
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    |dw:1354339128951:dw|

  2. Kelumptus
    • 3 years ago
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    is that x+1/n+1/x+1/x to infinity?

  3. Kelumptus
    • 3 years ago
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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...

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

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

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

  8. DLS
    • 3 years ago
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    @Algebraic! @ghazi @RadEn

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

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

  11. sirm3d
    • 3 years ago
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    find the derivative by implicit differentiation

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

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

  14. sirm3d
    • 3 years ago
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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

  15. DLS
    • 3 years ago
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    yeah i got that,what next

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

  17. sirm3d
    • 3 years ago
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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 -

  18. ghazi
    • 3 years ago
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    LHS --- left hand side RHS--- right hand side

  19. DLS
    • 3 years ago
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    lol i know that

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

  21. ghazi
    • 3 years ago
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    lol

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

  23. ghazi
    • 3 years ago
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    @DLS i guess you can do it now

  24. DLS
    • 3 years ago
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    what did u do with 1/y

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

  26. ghazi
    • 3 years ago
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    he differentiated it , implicitly

  27. DLS
    • 3 years ago
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    how did u get y^2

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

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

  30. DLS
    • 3 years ago
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    i know that too ! :o

  31. DLS
    • 3 years ago
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    okay whats the last step?

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

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