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Bryanluxor Group Title

why does: y+dy=(x+dx)^-2 equal: =x^-2(1+dx/x)^-2

  • 11 months ago
  • 11 months ago

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  1. RaphaelFilgueiras Group Title
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    put x in evidence

    • 11 months ago
  2. atlas Group Title
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    Another way of thinking is divide the expression on R.H.S with x^-2 and then multiply it with x^-2 on the outside

    • 11 months ago
  3. atlas Group Title
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    multiplying and dividing Right hand side with x^-2 \[\frac{ x ^{-2}(x+dx)^{-2} }{ x^{-2} }\] \[x^{-2} (\frac{ x+dx }{ x })^{-2}\]

    • 11 months ago
  4. atlas Group Title
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    simplify it to x^-2 (1+dx/x)^-2 I hope it makes sense now

    • 11 months ago
  5. Bryanluxor Group Title
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    I stiil dont get it Could someone please explain it step by step?

    • 11 months ago
  6. myininaya Group Title
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    Ok, do you agree that x+dx could be written as x(1+dx/x)?

    • 11 months ago
  7. myininaya Group Title
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    \[x+dx=x+\frac{x}{x} dx=x+x \cdot \frac{dx}{x}=x(1+\frac{dx}{x})\]

    • 11 months ago
  8. Bryanluxor Group Title
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    how can x+dx be written as x(1+dx/x)?

    • 11 months ago
  9. myininaya Group Title
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    \[(x+dx)^{-2}=[(x)(1+\frac{dx}{x})]^{-2}=x^{-2}(1+\frac{dx}{x})^{-2} \]

    • 11 months ago
  10. myininaya Group Title
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    Did you see what I said above what you said?

    • 11 months ago
  11. myininaya Group Title
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    |dw:1387637203504:dw|

    • 11 months ago
  12. myininaya Group Title
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    |dw:1387637215111:dw|

    • 11 months ago
  13. myininaya Group Title
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    you can factor out that x

    • 11 months ago
  14. Bryanluxor Group Title
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    but how did you get to x+x d/x? the equation is (x+dx)^-2

    • 11 months ago
  15. myininaya Group Title
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    You wanted step by step I'm looking at the inside, x+dx, right now.

    • 11 months ago
  16. Bryanluxor Group Title
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    ok

    • 11 months ago
  17. myininaya Group Title
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    If you can understand why x+dx=x(1+dx/x) we can move on to the exponent part

    • 11 months ago
  18. myininaya Group Title
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    which i already did above

    • 11 months ago
  19. myininaya Group Title
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    but i can redo

    • 11 months ago
  20. Bryanluxor Group Title
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    i dont understand why x+dx=x(1+dx/x)

    • 11 months ago
  21. Bryanluxor Group Title
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    where did you get the 1?

    • 11 months ago
  22. myininaya Group Title
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    Like do you the distributive property. It says: a(b+c)=ab+ac

    • 11 months ago
  23. Bryanluxor Group Title
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    and how did you get dx/x?

    • 11 months ago
  24. myininaya Group Title
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    x(1)=x

    • 11 months ago
  25. myininaya Group Title
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    \[x+dx=x+\frac{x}{x} dx \] look I multiply dx by x/x which is just one

    • 11 months ago
  26. myininaya Group Title
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    you should see an x in both terms now

    • 11 months ago
  27. myininaya Group Title
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    you can factor an x out

    • 11 months ago
  28. Bryanluxor Group Title
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    how did you get x/x?

    • 11 months ago
  29. myininaya Group Title
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    \[x(1+\frac{1}{x}dx)\] \[x(1+\frac{dx}{x}) \]

    • 11 months ago
  30. myininaya Group Title
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    I just put it there so you would see better x/x is there if you write it because it is just one

    • 11 months ago
  31. myininaya Group Title
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    If you factor something out you are dividing the terms you factor from

    • 11 months ago
  32. Bryanluxor Group Title
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    im sorry but i dont understnad

    • 11 months ago
  33. Bryanluxor Group Title
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    *understand

    • 11 months ago
  34. myininaya Group Title
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    For example \[3x+9=3(\frac{3x}{3}+\frac{9}{3})=3(x+3)\] Do you understand this example?

    • 11 months ago
  35. Bryanluxor Group Title
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    Can you please write down every step you do and how you get every variable?

    • 11 months ago
  36. Bryanluxor Group Title
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    in one answer please

    • 11 months ago
  37. myininaya Group Title
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    If you don't understand it separately how do you expect to understand it together?

    • 11 months ago
  38. myininaya Group Title
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    Do you understand the example I just put?

    • 11 months ago
  39. Bryanluxor Group Title
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    no sorry

    • 11 months ago
  40. Bryanluxor Group Title
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    im new to calculus

    • 11 months ago
  41. myininaya Group Title
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    You might want to review factoring then. Because all I did was factor 3x+9 in that example

    • 11 months ago
  42. Bryanluxor Group Title
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    i will

    • 11 months ago
  43. myininaya Group Title
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    Do you know the distributive property?

    • 11 months ago
  44. Bryanluxor Group Title
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    no sorry

    • 11 months ago
  45. myininaya Group Title
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    Like a(b+c) means ab+ac

    • 11 months ago
  46. Bryanluxor Group Title
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    yeah

    • 11 months ago
  47. myininaya Group Title
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    That is the distributive property

    • 11 months ago
  48. Bryanluxor Group Title
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    ok

    • 11 months ago
  49. myininaya Group Title
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    You can look at it either way. a(b+c)=ab+ac ab+ac=a(b+c) Do you see on this side they say hey both of these terms have an a in common so let's factor it out

    • 11 months ago
  50. Bryanluxor Group Title
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    ok

    • 11 months ago
  51. myininaya Group Title
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    What they are doing when they factor is pulling something out (multiplying) and then also dividing by what they pulled out. Like for example , ab+ac we could factor factor out ac but that means we also need to divide each term by ac like this: \[ac(\frac{ab}{ac}+\frac{ac}{ac})=ac(\frac{b}{c}+1)\]

    • 11 months ago
  52. myininaya Group Title
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    What do you get when you multiply out the ac(b/c+1) expression?

    • 11 months ago
  53. myininaya Group Title
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    i must go good luck

    • 11 months ago
  54. Bryanluxor Group Title
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    no idea

    • 11 months ago
  55. Bryanluxor Group Title
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    thankyou

    • 11 months ago
  56. OOOPS Group Title
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    I don't understand what we are supposed to do, re read your post, y +dy = (x+dx)^-2 equal = x^-2(1+dx/x)^-2 can you use the draw box below to write it again ?

    • 11 months ago
  57. OOOPS Group Title
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    and dy =y'? dx =x'?

    • 11 months ago
  58. Bryanluxor Group Title
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    \[y+dy=(x+dx)^{-2} =x ^{-2}(1+\frac{ dx }{ x })^{-2}\]

    • 11 months ago
  59. Bryanluxor Group Title
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    the aim is to differentiate y=x^2

    • 11 months ago
  60. OOOPS Group Title
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    2 equal signs?

    • 11 months ago
  61. Bryanluxor Group Title
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    the second equal sign is the result

    • 11 months ago
  62. Bryanluxor Group Title
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    once we have powered the left hand side of the equation to -2

    • 11 months ago
  63. Bryanluxor Group Title
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    what do you mean by "ODE?"

    • 11 months ago
  64. OOOPS Group Title
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    one more question: from which course , you have this problem?

    • 11 months ago
  65. Bryanluxor Group Title
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    its from a book called calculus made easy, ill post the page i found it on right now

    • 11 months ago
  66. OOOPS Group Title
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    thanks for information,

    • 11 months ago
  67. Bryanluxor Group Title
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    no problem

    • 11 months ago
  68. Bryanluxor Group Title
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    ill post the page in a sec

    • 11 months ago
  69. Bryanluxor Group Title
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    • 11 months ago
  70. Bryanluxor Group Title
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    he adds dy or dx to expand it a bit

    • 11 months ago
  71. OOOPS Group Title
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    I can understand (x +dx)^(-2) = x^(-2)(1+dx/x)^-2 but from y +dy , I cannot see how they get the right hand side. since y = x^-2 --> dy = -2x^-3 y + dy = x^-2 - 2 x^-3 = x^-2(1-2dx/x) which is not their right hand side :((

    • 11 months ago
  72. zpupster Group Title
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    this might clear it up i like this book his proofs are easier to understand than the way was taught.

    • 11 months ago
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