Need a little help--Instantaneous velocity: (derivatives) s=8t(squared)-10t+6; t=5. any help?,Thanks

- anonymous

Need a little help--Instantaneous velocity: (derivatives) s=8t(squared)-10t+6; t=5. any help?,Thanks

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- anonymous

Just use the sum rule. The derivative of a sum is the sum of the derivatives of each term.

- myininaya

s'=2*8t-10
s'(5)=16(5)-10

- anonymous

so s=156?

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## More answers

- anonymous

No, s'(5) = 156

- myininaya

s'(5)=80-10=70
did i miss something?

- anonymous

yeah, it's 70

- anonymous

I didn't check his arithmetic. In anycase, this is the trouble with just solving people's problems myininaya. They don't understand what you did, so they don't understand the answer, or how to do it again next time.

- anonymous

can you take it step by step for me ? now I am missing something , Thanks

- myininaya

do you know how to find the derivative?

- anonymous

yes

- myininaya

what is s' = then?

- anonymous

Prime

- myininaya

what is s'=______________?

- anonymous

oh - i got 156

- myininaya

the derivative of 8t^2 is?
the derivative of 10t is?
the derivative of constant is?

- myininaya

no clown i'm asking what is s'
not what s' at some number is

- anonymous

16t,10,0

- myininaya

so s'=16t+10+0=16t+10

- myininaya

oops s'=16t-10 i forgot the minus in the problem

- myininaya

so what is s' at t=5

- anonymous

Man your rough! but you make me think! ---- Thanks

- myininaya

i'm rough lol

- myininaya

do you get 70 now?

- anonymous

Hold on Im old!

- anonymous

yes, Thank you , Wow ! LOL

- myininaya

you really got it?
ok what's the instanteous velocity of s=t^4-6^2+3 at t=3

- anonymous

Oh and by the way I am a real clown, A Shriner Clown

- myininaya

s=t^4-6t^2+3

- myininaya

cool. lol

- anonymous

s=45?

- myininaya

what is s' ?

- anonymous

um, ok im lost ! Help!!

- myininaya

we want to find the instanteous velocity of s=t^4-6t^2+3 at t=3
finding velocity means we need to find the derivative of s
s' denotes the derivative
first let's break this up
what is the derivative of t^4?
what is the derivative of -6t^2?
what is the derivative of 3?

- anonymous

3t,12t,0

- anonymous

-12t oops

- myininaya

derivative of t^4 is 4*t^3
i used the power rule
everything else you got right
so 2/3 is passing

- anonymous

you funny and yes you are right about the first answer , you are making me think faster than normal! and making me nervous! I do not want to come off to you as a complete rock!

- myininaya

i'm sorry

- myininaya

lol take as much time as you need

- anonymous

ok, Thanks! Just wish sometimes I was better at this stuff, like you- I love smart math people!

- myininaya

clowns are cool too

- myininaya

let's put all the terms of s' together so
s'=?

- anonymous

ok, hold, please

- myininaya

k

- anonymous

s=96

- myininaya

i don't think thats right
and like polak said before its s'(3)=96
tell me what s' is first

- myininaya

s'(t)=

- anonymous

4(3)^3-12+3 Right?

- myininaya

s'(3)=4(3)^3-12(3)

- myininaya

remember we said the derivative of t^4 is 4t^3
the derivative of -6t^2 is -12t
the derivative of 3 is 0

- anonymous

OK!!!!! 3 is prime right?

- myininaya

yes 3 is prime
since 3 is a constant, its slope is zero, and since its slope is zero then the derivative of 3 is zero

- anonymous

we had a- 6t in the original problem? sorry my Bad yes we did, SO SORRY!

- anonymous

Hold on

- anonymous

s= 144+ 3?

- anonymous

or just 144?

- amistre64

ok...so whats our question?

- myininaya

s=t^4-6t^2+3
find velocity at t=3
i think hes getting mixed up on where things go

- amistre64

so clown; you say you can find a derivative; right?

- anonymous

I thought so, guess not

- amistre64

go ahead and give it a shot, i wanna see what you are doing

- amistre64

what is the derivative of:
t^4 -6^t +3 ??

- anonymous

Here is my problem..... s=8t^2 -10t +6; t=5

- amistre64

ok....lets work with 8t^2 -10t +6; what do you think the derivative should look like?

- anonymous

16t- 10 + 6

- amistre64

very close; the first and second terms are good; that last terms should be a 0 tho. do you know why?

- anonymous

because there is no constant?

- amistre64

does 6 = 6 t^0 ? and if so; how would you derive:
6 t^0?

- anonymous

Yes , due to the fact of the power 0

- amistre64

good;
then lets rewrite this in terms you can see :)
8t^2 -10t +6t^0; now derive that for me...

- anonymous

16t-10+6

- amistre64

16t is good;
-10 is excellent.
but 6 is wrong, you didnt derive it the same way you did the others ...why not?
derive 6t^0. in exactly the same way as you did the others. what do we get?

- anonymous

0

- amistre64

that is correct:)
so would you agree that our derivative is then:
16t-10 ?

- anonymous

Yes

- amistre64

ds
-- = 16t-10 very good; now when t=5, what does this equal?
dt

- anonymous

70!! I got it and you did not leave me at the train depot!!! YEA!!!!!

- amistre64

yay!!! :)

- anonymous

Thaank you very much!!!

- amistre64

youre welcome :)

- anonymous

Talk to ya soon maybe

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