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anonymous

  • 5 years ago

how do you find the derivative of (y+4)/(x-2)=5y at (3,1)???

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  1. amistre64
    • 5 years ago
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    either solve for "y" all by its little lonesome; or use implicit deriv..different.....that one word...

  2. amistre64
    • 5 years ago
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    lets try implicit... 5y = (y+4)/(x-2) ; take the d/dx of both sides.. (d/dx)(5y) = (d/dx)[(y+4)/(x-2)]

  3. amistre64
    • 5 years ago
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    5y' = apply quotient rule to this side 5y' = [(x-2)(1y') - (y+4)(x')] / [(x-2)^2] ; dy/dx = y' ; x' = 1

  4. amistre64
    • 5 years ago
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    get y' by itself if you dare :)

  5. anonymous
    • 5 years ago
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    no easier way? how can you get y by it self

  6. amistre64
    • 5 years ago
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    lol.... I get: y+4 y' = ------ x-7

  7. anonymous
    • 5 years ago
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    how??

  8. amistre64
    • 5 years ago
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    plug in (3,1) y' = -5/6 ?? where did I lose ya? :)

  9. amistre64
    • 5 years ago
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    y' = -5/4 ; forgot how to add lol

  10. anonymous
    • 5 years ago
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    how did you get to y+4/x-7

  11. amistre64
    • 5 years ago
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    by using paper and pencil really... but lets see if I can type it out...

  12. amistre64
    • 5 years ago
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    (x-2)(1y') - (y+4)(x') 5y' = ---------------- ; move (x-2)^2 up and bring y' down.. (x-2)^2 (x-2)(y') - (y+4) 5(x-2)^2 = ---------------- ; split the fraction.... y' (x-2)(y') (y+4) 5(x-2)^2 = ------- - ------- ; cancel top to bottom your y' y' y' (y+4) 5(x-2)^2 = (x-2) - ------- ; now subtract (x-2) from both sides y' - (y+4) [5(x-2)^2]-(x-2) = ------- ; I forgot something on the paper.... y'

  13. amistre64
    • 5 years ago
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    regardless tho, lets work this out: -4-y y' = ---------------- [5(x-2)^2] - (x-2) try that one :)

  14. amistre64
    • 5 years ago
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    (x=3,y=1) y' = (-4-1) / [5(3-2)^2 - (3-2)] y' = -5 / 4 , is that right?

  15. amistre64
    • 5 years ago
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    HAH!!! I got the same answer as I did with the last one lol

  16. anonymous
    • 5 years ago
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    yessss thank you so much

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