anonymous 5 years ago kk then, what is deriative??

1. anonymous

study of how a function change, or tangent line

2. amistre64

derivative is what is used to describe how one thing changes with respect to another

3. anonymous

hmmm.

4. anonymous

It is like a slope

5. amistre64

in the equation: y = 3x+2, the rate at which y changes with respect to x is '3'

6. amistre64

for every change in 'x', 'y' changes by 3

7. anonymous

hmm then u mean 2y=3x+3+2 ??

8. amistre64

not quite

9. anonymous

or 2y=6x+2?? (the 2 is const in this equetion?

10. amistre64

if you multiply the left by 2 the rights gotta be multiplied by 2 as well

11. amistre64

thats more of a scaling notion

12. amistre64

the derivative has to do with the change in y with respect to x when there is 'no' change in x

13. anonymous

hmmm

14. amistre64

$\lim_{h -> 0}\frac{(f(x+h)-f(x)}{(x+h)-(x)}$

15. amistre64

the derivative of: 3x+2 is then (3(x+h)+2) - (3x+2) ----------------- ; when h=0 x+h-x

16. amistre64

3x+3h+2 -3x-2 -------------- ; when h=0 h 3h --- ; when h=0 h 3 ; when h=0

17. anonymous

hmmm

18. amistre64

so the rate of change of a linear function is just the slope of the line

19. anonymous

hmmm

20. amistre64

the rate of change at any given point of a quadratic function is the slope of the line at a given point that is defined as the lim{h ->0} (f(x+h)-f(x)//h)

21. amistre64

x^2+x-3 ; how fast is y changing when x = 4?

22. anonymous

can you answer it? i think i can'T do it yet

23. amistre64

$\lim_{h -> 0}\frac{ [(x+h)^2 +(x+h)-3]-[x^2+x-3]}{x+h-x}$

24. amistre64

$\lim{x^2+h^2 +2xh +x+h-3-x^2-x-3 \over h}$

25. anonymous

okay give me a min

26. anonymous

getting my pencil and notebook

27. amistre64

that last 3 shoud be +3

28. anonymous

kk

29. anonymous

h^2 + 2xh + h / h

30. amistre64

$(x^2-x^2)+(x-x)+(-3+3)+(2xh+h) \over h$

31. amistre64

yes, i missed the ^2 on the h; you are roght

32. anonymous

:D

33. amistre64

$\lim_{h \rightarrow 0}\left({h^2\over h}+{2xh\over h}\right)$

34. anonymous

now we give x 3??

35. amistre64

when x=4 :)

36. amistre64

and I think we dropped an h someplace in the writing

37. anonymous

ahh missed 4 xd

38. anonymous

yes why don'T we do it one a more simple func??

39. amistre64

$\lim_{h ->0}({2xh\over h}+{h\over h}+{h^2\over h})$

40. amistre64

the simple function was the linear lol

41. amistre64

now when h=0 we get the equation of the derivative: 2x+1

42. amistre64

at x=4; y is changing at a rate of 9 with respect to each x

43. amistre64

the quick way after being taught all the limit definitions and the long way; is to use the power rule: x^2 +x -3 -> 2x +1

44. anonymous

hmm ^^ so that can we use this for another thing?

45. anonymous

with another func i mean

46. anonymous

(don't got the power rule can you explain?)

47. amistre64

yes; the derivative of position tells you velocity at a given point; the derivative of velocity tells you the acceleration at any given point

48. amistre64

the power rule is just the 'pattern' that occurs from doing derivatives the long way..

49. anonymous

oO

50. amistre64

$Cx^n \implies C*nx^{n-1}$ $5x^3 \implies 5*3x^{3-1} \iff 15x^2$

51. amistre64

which way would you do derivatives? the limit way or the power rule?

52. amistre64

$\begin{array}c 5x^4&+x^2&-4x^0\\20x^3&+2x&+0\end{array}$

53. anonymous

hmm i think limit way

54. amistre64

ok; do that the limit way... $\frac{[5(x+k)^4+(x+h)^2-4]-[5x^4+x^2-4]}{h}$

55. anonymous

which equetion we doing??

56. amistre64

f(x) = $$5x^4 +x^2 -4$$ the limit way

57. amistre64

except for it should say 5(x+h)^4 lol

58. amistre64

the power rule is quicker, easier, and just as precise

59. anonymous

ok :=)

60. anonymous

then do it in power rule ^^ if its that trustworthy

61. amistre64

the power rule is the 'patter' that you discover after doing about a thousand limit ways

62. anonymous

it was Cx^n = C x nx^n-1

63. amistre64

yes

64. anonymous

ok

65. anonymous

then for 5(x+4)^4 its >>>> 5 x 4(x)^3 ???

66. anonymous

hey you there?

67. amistre64

ok.... you trying to use the x+h in that?

68. anonymous

no i tried to use power rule that i did C.nx^n-1

69. amistre64

5x^4 ; try it on that one ...

70. anonymous

oka wait

71. anonymous

5 x 4(x)^3

72. anonymous

5 . 4.x^3

73. anonymous

true?

74. amistre64

true; now put it all together; 20x^3

75. anonymous

yess i got it??

76. amistre64

you did; the power rule takes a complicated form and reduces it to simple math

77. anonymous

yes its really usefull :) to you, am i good at maths?

78. amistre64

you can be good at maths if you wanna be :)

79. anonymous

:) really want to be ^^ i want to learn highschool units before i go to hichschool ^^

80. anonymous

really thanks amistre :)

81. amistre64

youre welcome :) keep up the practics

82. anonymous

normally just searching questions on Hz. google xd

83. amistre64

some good free practice can be had at interactmath.com

84. anonymous

ok ty