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anonymous

  • 5 years ago

find second derivative if (x-5)^5+(y-2)^5=64

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  1. amistre64
    • 5 years ago
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    f1{x,y} = 5(x-5)^4 f11{x,y} = 20(x-5)^3

  2. amistre64
    • 5 years ago
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    f2{x,y} = 5(y-2)^4 f22{x,y} = 20(y-2)^3

  3. anonymous
    • 5 years ago
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    5(x-5)^4 + 5(y-2)^4 dy/dx =0 ist derivative

  4. amistre64
    • 5 years ago
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    right, so long as we imply that y is a function of x

  5. anonymous
    • 5 years ago
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    yes,, maybe we can let snenlaha do the 2nd derivative hehehehe

  6. amistre64
    • 5 years ago
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    maybe :)

  7. anonymous
    • 5 years ago
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    i couldn't continue from the first to the 2nd derivative

  8. anonymous
    • 5 years ago
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    but do you know the process of the ist that i did?

  9. anonymous
    • 5 years ago
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    yes i do and i got it the same as yours

  10. anonymous
    • 5 years ago
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    ok try the second so that you cn have confidence in yourself

  11. anonymous
    • 5 years ago
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    do i need to make dy/dx a subject of the formula

  12. anonymous
    • 5 years ago
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    try to arrange them first, start with dy/dx =

  13. amistre64
    • 5 years ago
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    you can; y' just derives to y''; just be sure to use it as such in its product rule

  14. anonymous
    • 5 years ago
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    yes thats the other way doing it,, either one will arrive at the right solution

  15. amistre64
    • 5 years ago
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    to implicit it again would be easier; no quotient ruls to fight with i believe

  16. anonymous
    • 5 years ago
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    ok thats rigth....try implicitly ..

  17. amistre64
    • 5 years ago
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    5(x-5)^4 + 5(y-2)^4 y' =0 20(x-5)^3 + 5(y-2)^4 y'' + 20(y-2)^3 y' y' = 0 then if it works out that way :)

  18. anonymous
    • 5 years ago
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    Dx(5(x-5)^4) + Dx(5(y-2)^4 dy/dx) =Dx(0).......ok amistre did it now hehehehe

  19. amistre64
    • 5 years ago
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    i got no idea if its right :)... other than the obvious typos that is -20[(x-4)^3 + (y-2)^3 y'^2] y'' = ------------------------- right? 5(y-2)^3

  20. amistre64
    • 5 years ago
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    -20/5 reduces..... and y' = whatever it equals lol

  21. anonymous
    • 5 years ago
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    the answer is suppose to be: y''=(-256(X-5)^3)/(y-2)^9

  22. anonymous
    • 5 years ago
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    dy/dx=-(x-5)^{4}/(y-2)^{4}\[d ^{2}y/dx ^{2}=-256(x-5)^{3}/(y-2)^{5}\]

  23. amistre64
    • 5 years ago
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    it prolly simplifies to that then lol...

  24. anonymous
    • 5 years ago
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    yeah ,... thats the answer to it Snenhlala....try to practice till you arrive to that answer

  25. anonymous
    • 5 years ago
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    sorry the denominator for the second derivative should read (y-2)^9

  26. anonymous
    • 5 years ago
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    did you used product rule or quotient rule to find 2nd derivative

  27. anonymous
    • 5 years ago
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    i did mine in quotient rule

  28. anonymous
    • 5 years ago
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    use the quotient rule and sub for dy/dx

  29. anonymous
    • 5 years ago
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    mulitply each term by (y-2)^4 then factor -4(x-5)^3(y-2)^3 this will leave (x-5)^5+(y-2)^4 which equals 64 (from the original equation)

  30. anonymous
    • 5 years ago
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    should read (x-5)^5+ (y-2)^5 which equals 64

  31. anonymous
    • 5 years ago
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    should i start to multiply from the 1st derivative or from the origin equation?

  32. anonymous
    • 5 years ago
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    multiply the second derivative

  33. anonymous
    • 5 years ago
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    by (y-2)^4

  34. anonymous
    • 5 years ago
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    y'= -(x-5)^4 / (y-2)^4 -4(y-2)^4 (x-5)^3 - 4(x-5)^4 (y-2)^3 y' y"= ----------------------------------- now subst. y ' in this equqtion ((y-2)^4)^2 -4(y-2)^4 (x-5)^3 - 4(x-5)^4 (y-2)^3 [-(x5^4)/(y-2)^4] y"= ------------------------------------------------------------- ((y-2)^4)^2 -4(y-2)^4 (x-5)^3 + 4(x-5)^8 (y-2) y"= ----------------------------------- (y-2)^8

  35. anonymous
    • 5 years ago
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    -4(y-2)^4 (x-5)^3 + 4(x-5)^8/(y-2) y"= ----------------------------------- ... sorry its divided by y-2 (y-2)^8

  36. anonymous
    • 5 years ago
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    -4(y-2)^5 (x-5)^3 + 4(x-5)^8 y"= ----------------------------------- (y-2)^9

  37. anonymous
    • 5 years ago
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    -4 (x-5)^3 [(y-2)^5 + (x-5)^5] y"= ----------------------------------- (y-2)^9

  38. anonymous
    • 5 years ago
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    -4 (x-5)^3 [64] y"= -------------- (y-2)^9 57 seconds ago

  39. anonymous
    • 5 years ago
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    -256 (x-5)^3 y"= -------------- (y-2)^9

  40. anonymous
    • 5 years ago
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    well i think thats it hehehe

  41. anonymous
    • 5 years ago
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    thank you

  42. anonymous
    • 5 years ago
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    w.c.

  43. anonymous
    • 5 years ago
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    did you arrived in the same procedure?

  44. anonymous
    • 5 years ago
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    and of course the same answer? lol

  45. anonymous
    • 5 years ago
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    yes i did arrive but it too tricky

  46. anonymous
    • 5 years ago
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    yeah kind of hehehe,,

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