Question

@hartnn

Answer 1

im stuck, plz explain?

Answer 2

derivative of x^n is ?

Answer 3

x?

Answer 4

no
i'm sure you've come across this formula :
\(\Large \dfrac{d}{dx} x^n = n x^{n-1}\)

Answer 5

oh yeah

Answer 6

differentiate it one more time to get the 2nd derivative

Answer 7

differentiate nx^n-1?

Answer 8

yes

Answer 9

is that a difficult task for ya ?

Answer 10

Should we multiply it or not @hartnn

Answer 11

not required

Answer 12

Then product rule?

Answer 13

nopes, we just find the co-efficient of x^4 term
12 times that will give you the co-efficient of x^2 term in f''(x)

why ? that i am trying to explain her

Answer 14

oh ok im trying to do it so chill
@hartnn

Answer 15

Oh I am getting you.. :)

Answer 16

what do you mean coefficient of x^4

Answer 17

if you multiply both terms in f(x), it will have all exponents from x^6 to constant, right ?

so it will have a x^4 term too, isn't it ?

Answer 18

for example if you multiply
3x^2 and (-6x^2)

you will get -18 x^4
here, -18 is called the co-efficient of x^4

Answer 19

but i dont get why i wouldnt multiply?

Answer 20

you can, thats a longer method.

Answer 21

if you want to, go ahead and multiply :)
and tell me what did you get the co-efficient of x^4 as

Answer 22

so muliplying the first two i would get 3x^5 right?

Answer 23

id rather learn the shorter method ahahhaha

Answer 24

why would u multiply x^3 and 3x^2 ?

Answer 25

i thought thats what you said to do, ok nvm

Answer 26

i asked for the 2nd derivative of x^n :P

that too if you want to know why..

Answer 27

how do i find the second derivative D;

Answer 28

by differentiating the 1st derivative

Answer 29

derivative of (n x^{n-1})
is ?

Answer 30

Did we find both pieces that lead to x^4?

Answer 31

one, i found it for her, other was expecting she will find on her own

Answer 32

clearly, your derivative skills are not upto the mark for attempting this question.
please practice as many derivatives questions as you can...!

Answer 33

Fair enough. Just wondering if it was headed that way. :-)

Answer 34

thanks lol @hartnn

Answer 35

let me start asking simple questions

what is derivative of x^2
can u find ?

Answer 36

She can tell, I bet..!! :P

Answer 37

you taught her ? ;)

Answer 38

nx^n-1 (:

Answer 39

thats for x^n

i asked for x^2

Answer 40

I said "Can", but she won't.. :P

Answer 41

2x

Answer 42

He he he.. you saw?? :P

Answer 43

i suspect you gave her the answer in a private message :P

Answer 44

@waterineyes can you please leave

Answer 45

are you calling me stupid?

Answer 46

no one is calling you anything

Answer 47

@mondona it is always the case that you hate me??

Answer 48

@mondona
moving ahead

can you tell me the derivative of x^4 ??

Answer 49

Why are you not saying anything to hartnn, he blamed me and you for having answer through private message.. :P

Answer 50

4 (x^3)

Answer 51

Go ahead, I am leaving.. :)

Answer 52

thank you

Answer 53

now can you tell me the derivative of

4x^3 ?

Answer 54

3(4x^2)

Answer 55

4 (3x^2)
yes
which is 12x^2, right ?

Answer 56

yes

Answer 57

so the derivative of x^4 = 4x^3

derivative of 4x^3 = 12x^2

so derivative of derivative of x^4 is 12x^2

means 2nd derivative of x^4 is 12 x^2

makes sense ?

Answer 58

so the answer my question is looking for is 12x^2?

Answer 59

its just asking for the 2nd derivative?

Answer 60

Why would the 2nd derivative of x^4 be the answer to your question? You need the x^4 term in your original expression, not an example problem.

Answer 61

oh so just 12

Answer 62

i did all that so that you know why we need to multiply the co-efficient of x^4 by 12 :P

question asked for co-efficient of x^2

it will be 12 times the co-efficient of x^4

why ?
because 2nd derivative of x^4 is 12x^2

Answer 63

i get confused when 5 people start coming in lol

Answer 64

so what is @tkhunny talking about

Answer 65

You are still missing the "in your original expression" part.
Do NOT use the example problem to answer your question.

Answer 66

"co-efficient of x^2 will be 12 times the co-efficient of x^4"
did you get this part ?

Answer 67

yes

Answer 68

if so, just find the co-efficient of x^4 for f(x)

Answer 69

of nx^n-1 is ^

Answer 70

n(nx^-1)

Answer 71

this is honestly taking much more time than it should lol idk what youre saying

Answer 72

derivative of nx^n-1 is n(nx^-1)

Answer 73

we are past that

find f(x)

Answer 74

(x^3 +3x^2 +3) (3x^3 - 6x^2 -8x+1) = ... ?

Answer 75

SO NOW YOURE TELLING ME TO SOLVE IT?! you told me not to earlier!!!!!

Answer 76

@tkhunny can you please help me

Answer 77

thats the longer way , remember ?

i don't think you'll get the shorter way

Answer 78

so what were we talking about earlier? was that just wasting my time??

Answer 79

as already told, that was to explain why are we finding the co-efficient of x^4
and why we will multiply it by 12

Answer 80

3-24 x-15 x^2-14 x^3-26 x^4+3 x^5+3 x^6

Answer 81

now what

Answer 82

correct, so whats the co-efficient of x^4 from there ?

Answer 83

Whoa! Settle down, there. Unique answers don't care how you find them. There may be several ways to proceed. In my opinion, hartnn's original way was BY FAR the best way. However, you didn't seem to be getting it. It would have been great if you had been getting it. So, this is where we are...

1) Let's just multiply out the entire expression.
2) When you gnerate all nine pieces of the multiplication, look at the two pieces that contributed to x^4.
3) Stop and think a little about how we might have found those two pieces without multiplying the entire expressions.
4) In any case, once we have the WHOLE of the x^4 term, the 2nd derivative shoudl be no problem, using the usual polynomial rule.

Answer 84

*12 pieces

Answer 85

Whoops! 12 pieces.

Answer 86

you there ? you're just one step away from the answer...

Answer 87

sorry idk why openstudy keeps on disconnecting

Answer 88

the co-efficient of x^4 from that
3-24 x-15 x^2-14 x^3-26 x^4+3 x^5+3 x^6
is ?

Answer 89

-26

Answer 90

right?

Answer 91

yes
now just multiply it by 12
and done!

Answer 92

wait is it 26 or -26?

Answer 93

i think i messed up

Answer 94

312

Answer 95

-26