Question

kk then, what is deriative??

Answer 1

study of how a function change, or tangent line

Answer 2

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

Answer 3

hmmm.

Answer 4

It is like a slope

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

not quite

Answer 9

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

Answer 10

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

Answer 11

thats more of a scaling notion

Answer 12

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

Answer 13

hmmm

Answer 14

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

Answer 15

the derivative of: 3x+2 is then

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

Answer 16

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


3h
--- ; when h=0
h

3 ; when h=0

Answer 17

hmmm

Answer 18

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

Answer 19

hmmm

Answer 20

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)

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

okay give me a min

Answer 26

getting my pencil and notebook

Answer 27

that last 3 shoud be +3

Answer 28

kk

Answer 29

h^2 + 2xh + h / h

Answer 30

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

Answer 31

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

Answer 32

:D

Answer 33

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

Answer 34

now we give x 3??

Answer 35

when x=4 :)

Answer 36

and I think we dropped an h someplace in the writing

Answer 37

ahh missed 4 xd

Answer 38

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

Answer 39

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

Answer 40

the simple function was the linear lol

Answer 41

now when h=0 we get the equation of the derivative:

2x+1

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

with another func i mean

Answer 46

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

Answer 47

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

Answer 48

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

Answer 49

oO

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

hmm
i think limit way

Answer 54

ok; do that the limit way...

\[\frac{[5(x+k)^4+(x+h)^2-4]-[5x^4+x^2-4]}{h}\]

Answer 55

which equetion we doing??

Answer 56

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

Answer 57

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

Answer 58

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

Answer 59

ok :=)

Answer 60

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

Answer 61

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

Answer 62

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

Answer 63

yes

Answer 64

ok

Answer 65

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

Answer 66

hey you there?

Answer 67

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

Answer 68

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

Answer 69

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

Answer 70

oka wait

Answer 71

5 x 4(x)^3

Answer 72

5 . 4.x^3

Answer 73

true?

Answer 74

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

Answer 75

yess i got it??

Answer 76

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

Answer 77

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

Answer 78

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

Answer 79

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

Answer 80

really thanks amistre :)

Answer 81

youre welcome :) keep up the practics

Answer 82

normally just searching questions on Hz. google xd

Answer 83

some good free practice can be had at interactmath.com

Answer 84

ok ty