## Bryanluxor Group Title why does: y+dy=(x+dx)^-2 equal: =x^-2(1+dx/x)^-2 7 months ago 7 months ago

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1. RaphaelFilgueiras Group Title

put x in evidence

2. atlas Group Title

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

3. atlas Group Title

multiplying and dividing Right hand side with x^-2 $\frac{ x ^{-2}(x+dx)^{-2} }{ x^{-2} }$ $x^{-2} (\frac{ x+dx }{ x })^{-2}$

4. atlas Group Title

simplify it to x^-2 (1+dx/x)^-2 I hope it makes sense now

5. Bryanluxor Group Title

I stiil dont get it Could someone please explain it step by step?

6. myininaya Group Title

Ok, do you agree that x+dx could be written as x(1+dx/x)?

7. myininaya Group Title

$x+dx=x+\frac{x}{x} dx=x+x \cdot \frac{dx}{x}=x(1+\frac{dx}{x})$

8. Bryanluxor Group Title

how can x+dx be written as x(1+dx/x)?

9. myininaya Group Title

$(x+dx)^{-2}=[(x)(1+\frac{dx}{x})]^{-2}=x^{-2}(1+\frac{dx}{x})^{-2}$

10. myininaya Group Title

Did you see what I said above what you said?

11. myininaya Group Title

|dw:1387637203504:dw|

12. myininaya Group Title

|dw:1387637215111:dw|

13. myininaya Group Title

you can factor out that x

14. Bryanluxor Group Title

but how did you get to x+x d/x? the equation is (x+dx)^-2

15. myininaya Group Title

You wanted step by step I'm looking at the inside, x+dx, right now.

16. Bryanluxor Group Title

ok

17. myininaya Group Title

If you can understand why x+dx=x(1+dx/x) we can move on to the exponent part

18. myininaya Group Title

which i already did above

19. myininaya Group Title

but i can redo

20. Bryanluxor Group Title

i dont understand why x+dx=x(1+dx/x)

21. Bryanluxor Group Title

where did you get the 1?

22. myininaya Group Title

Like do you the distributive property. It says: a(b+c)=ab+ac

23. Bryanluxor Group Title

and how did you get dx/x?

24. myininaya Group Title

x(1)=x

25. myininaya Group Title

$x+dx=x+\frac{x}{x} dx$ look I multiply dx by x/x which is just one

26. myininaya Group Title

you should see an x in both terms now

27. myininaya Group Title

you can factor an x out

28. Bryanluxor Group Title

how did you get x/x?

29. myininaya Group Title

$x(1+\frac{1}{x}dx)$ $x(1+\frac{dx}{x})$

30. myininaya Group Title

I just put it there so you would see better x/x is there if you write it because it is just one

31. myininaya Group Title

If you factor something out you are dividing the terms you factor from

32. Bryanluxor Group Title

im sorry but i dont understnad

33. Bryanluxor Group Title

*understand

34. myininaya Group Title

For example $3x+9=3(\frac{3x}{3}+\frac{9}{3})=3(x+3)$ Do you understand this example?

35. Bryanluxor Group Title

Can you please write down every step you do and how you get every variable?

36. Bryanluxor Group Title

37. myininaya Group Title

If you don't understand it separately how do you expect to understand it together?

38. myininaya Group Title

Do you understand the example I just put?

39. Bryanluxor Group Title

no sorry

40. Bryanluxor Group Title

im new to calculus

41. myininaya Group Title

You might want to review factoring then. Because all I did was factor 3x+9 in that example

42. Bryanluxor Group Title

i will

43. myininaya Group Title

Do you know the distributive property?

44. Bryanluxor Group Title

no sorry

45. myininaya Group Title

Like a(b+c) means ab+ac

46. Bryanluxor Group Title

yeah

47. myininaya Group Title

That is the distributive property

48. Bryanluxor Group Title

ok

49. myininaya Group Title

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

50. Bryanluxor Group Title

ok

51. myininaya Group Title

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: $ac(\frac{ab}{ac}+\frac{ac}{ac})=ac(\frac{b}{c}+1)$

52. myininaya Group Title

What do you get when you multiply out the ac(b/c+1) expression?

53. myininaya Group Title

i must go good luck

54. Bryanluxor Group Title

no idea

55. Bryanluxor Group Title

thankyou

56. OOOPS Group Title

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 ?

57. OOOPS Group Title

and dy =y'? dx =x'?

58. Bryanluxor Group Title

$y+dy=(x+dx)^{-2} =x ^{-2}(1+\frac{ dx }{ x })^{-2}$

59. Bryanluxor Group Title

the aim is to differentiate y=x^2

60. OOOPS Group Title

2 equal signs?

61. Bryanluxor Group Title

the second equal sign is the result

62. Bryanluxor Group Title

once we have powered the left hand side of the equation to -2

63. Bryanluxor Group Title

what do you mean by "ODE?"

64. OOOPS Group Title

one more question: from which course , you have this problem?

65. Bryanluxor Group Title

its from a book called calculus made easy, ill post the page i found it on right now

66. OOOPS Group Title

thanks for information,

67. Bryanluxor Group Title

no problem

68. Bryanluxor Group Title

ill post the page in a sec

69. Bryanluxor Group Title

70. Bryanluxor Group Title

he adds dy or dx to expand it a bit

71. OOOPS Group Title

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 :((

72. zpupster Group Title

this might clear it up i like this book his proofs are easier to understand than the way was taught.