anonymous
  • anonymous
Please help me math talent!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
If you say so.
anonymous
  • anonymous
Thank you!
anonymous
  • anonymous
You're welcome.

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anonymous
  • anonymous
\[w=\frac{ \sqrt(x) }{ 2^2+t3^t } \]
anonymous
  • anonymous
sorry it should be sart (t)
anonymous
  • anonymous
and find dw/dt
anonymous
  • anonymous
that is simple
anonymous
  • anonymous
do u want the answer or do u want a step by step solution?
anonymous
  • anonymous
when u answer my question i sill proceed
anonymous
  • anonymous
Math, you can't simply give them the answer. It's against CoC. Guide them to it, so they can answer it themselves.
anonymous
  • anonymous
step by step pleae!
anonymous
  • anonymous
*please
.Sam.
  • .Sam.
Quotient rule with respect to (t)..
anonymous
  • anonymous
g(x)f(x)'-f(x)g(x)'/g(x)^2
.Sam.
  • .Sam.
This right\[w=\frac{\sqrt{x}}{3^t t+2^2}\]
.Sam.
  • .Sam.
You can use chain rule as well
anonymous
  • anonymous
therefore, (2t62+t3^t)d/dx(sqrt(t)-sqrt(t)(2t^2+t3^t)/(2t^2+t3^t)^2
.Sam.
  • .Sam.
Followed by product rule
anonymous
  • anonymous
I dont how how to caculate the root.
anonymous
  • anonymous
and how to do (2t62+3t^3) to derivative?
.Sam.
  • .Sam.
The root "x" is just acted like constant, ignore it
anonymous
  • anonymous
my teacher told me to do something like 1/2x^-1/2? is it wrong
.Sam.
  • .Sam.
is the question this?\[\Large w=\frac{\sqrt{x}}{3^t t+2^2}\]
anonymous
  • anonymous
no \[w=\frac{ Sqrt(t) }{ 2t^2+t3^t }\]
.Sam.
  • .Sam.
You sure? the answer is \[\Large \frac{dw}{dt}=-\frac{3^t+t \left(3^t (9 \log )+6\right)}{2 t^{3/2} \left(2 t+3^t\right)^2}\]
anonymous
  • anonymous
no you dont use log. i have not learnt that yet
.Sam.
  • .Sam.
\[\Large \frac{dw}{dt}=-\frac{3^t+t \left(3^t ( \ln(9) )+6\right)}{2 t^{3/2} \left(2 t+3^t\right)^2}\] This?
anonymous
  • anonymous
mm maybe but is it possible to go simpler than this?
anonymous
  • anonymous
is it not possible?
.Sam.
  • .Sam.
no its not possible, other results are
1 Attachment
anonymous
  • anonymous
I only have learned power rule, exponential rule and product rule. ( chain rule)
anonymous
  • anonymous
step one use the quotient rule..
anonymous
  • anonymous
the only trick u have here is 3^t, u may use the table or D-operator...
anonymous
  • anonymous
yes I did! its above. I dont know how to break down and power rules.
anonymous
  • anonymous
please show me step by step.
anonymous
  • anonymous
let me show u how to solve 3^t
anonymous
  • anonymous
is that the part ur are struggling with right
anonymous
  • anonymous
i will show u step by step but let's break this down
anonymous
  • anonymous
Yes :( t3^t
anonymous
  • anonymous
thank you so much. I want to cry right now
anonymous
  • anonymous
stop crying and fight for the answer
anonymous
  • anonymous
ok, i wil! thanks
anonymous
  • anonymous
trust me i will let u solve this problem
anonymous
  • anonymous
you wont help me?
anonymous
  • anonymous
so far i have got
anonymous
  • anonymous
damn i wrote the answer on another post hehehe
anonymous
  • anonymous
\[\[u = 3^t, \space du = 3^t \ln(3)\]\]
anonymous
  • anonymous
\[\frac{ (2t^2+t3^t)(\sqrt(x)'-\sqrt(x)(2t^2+t3^t) }{ (2t^2+t3^t)^2 }\]
anonymous
  • anonymous
\[u = 3^t, \space du = 3^t \ln(3)\]
anonymous
  • anonymous
now do u know how this happend
anonymous
  • anonymous
but its t3^t?
anonymous
  • anonymous
forget the t for now because i want to show u bit by bit
anonymous
  • anonymous
because with the t we will get into the product rule
anonymous
  • anonymous
ok, I got it. i am taking note hold on
anonymous
  • anonymous
du_3^t why its In(3)?
anonymous
  • anonymous
good question, now u r starting to listen and that is a good sign of learning...
anonymous
  • anonymous
u= 3^t what happens if you take the natural log of both sides?
anonymous
  • anonymous
mm im not sure, , negative numbers?
anonymous
  • anonymous
ln(u) = ln(3^t)
anonymous
  • anonymous
now do u know how to differentiate both sides?
anonymous
  • anonymous
No I am not sure.
anonymous
  • anonymous
mutiply?
anonymous
  • anonymous
ok no problem, first of all we need some log rules
anonymous
  • anonymous
ln(u) = tln(3)
anonymous
  • anonymous
did u see what happend to t?
anonymous
  • anonymous
power of t went outside of 3 and In?
anonymous
  • anonymous
yes this is a primitive ln rule
anonymous
  • anonymous
Oh I see.
anonymous
  • anonymous
Do i use this everytime i do product?
anonymous
  • anonymous
now if y=ln(x) what is y'?
anonymous
  • anonymous
u mean every time u have a log of a power?
anonymous
  • anonymous
ok, I got it.
anonymous
  • anonymous
sorry power of a log
anonymous
  • anonymous
now if y=ln(x) what is y'?
anonymous
  • anonymous
power of a log, ok !
anonymous
  • anonymous
mmm.. y=In/(x)?
anonymous
  • anonymous
no y=ln(x) ->y'=1/x
anonymous
  • anonymous
wow, thats new to me!
anonymous
  • anonymous
this is basic differentiation of natural log
anonymous
  • anonymous
so now back to our question ln(u) = tln(3) differentiate both sides...
anonymous
  • anonymous
tIn(3)/x
anonymous
  • anonymous
ok let me make this even simple
anonymous
  • anonymous
so u don't get confused
anonymous
  • anonymous
thanks for taking your time.
anonymous
  • anonymous
\[\frac{d}{dt}a^t=a^tln(a)\]
anonymous
  • anonymous
can u memorize this for now and take it for granted
anonymous
  • anonymous
Ok,
anonymous
  • anonymous
ok use this formula and tell me what is 3^t?
anonymous
  • anonymous
hint: a=3
anonymous
  • anonymous
mmm.... 3^tIn(3)?
anonymous
  • anonymous
well done so memorize that please take a note and keep it in ur mind the same way u know ur name...
anonymous
  • anonymous
Ok I will.
anonymous
  • anonymous
whats the next step?
anonymous
  • anonymous
sorry i was replying to another post on set theory ok
anonymous
  • anonymous
its okay.
anonymous
  • anonymous
now tell me how would u differentiate? \[ 2^2+t3^t \]
anonymous
  • anonymous
you mean 2t^2?
anonymous
  • anonymous
2^tIn(2)+3tIn(3)?
anonymous
  • anonymous
no 2^2 is a constant
anonymous
  • anonymous
look at it again
anonymous
  • anonymous
trust me by solving this part we are more than half way of solving the problem
anonymous
  • anonymous
\[2^2+t3^t\]
anonymous
  • anonymous
2^2=4 so when u differentiate a constant u get zero right!?
anonymous
  • anonymous
Oh! so its (4t)?
anonymous
  • anonymous
ok listen let me solve it
anonymous
  • anonymous
can u see how this happened?
anonymous
  • anonymous
using the product rule
anonymous
  • anonymous
No, wheres 2 go? theres no 2 in the answer
anonymous
  • anonymous
\[u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt\]
anonymous
  • anonymous
listen y=4, what is y'?
anonymous
  • anonymous
y=-4?
anonymous
  • anonymous
zero? beacuse its constant
anonymous
  • anonymous
zero well done, so y=2^2, y'=?
anonymous
  • anonymous
zero?
anonymous
  • anonymous
yes well done
anonymous
  • anonymous
so differentiate now t3^t
anonymous
  • anonymous
3^3In(t)?
anonymous
  • anonymous
no its 3 ^tIn(3)?
anonymous
  • anonymous
\[u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt\]
anonymous
  • anonymous
do u know the product rule?
anonymous
  • anonymous
I am not sure
anonymous
  • anonymous
uv'+u'v???
anonymous
  • anonymous
do u know that rule?
anonymous
  • anonymous
yes I do qutiotinent rule?
anonymous
  • anonymous
no i said product rule..
anonymous
  • anonymous
do u want me to solve the whole thing then u may go and think about it?
anonymous
  • anonymous
sorry no.
anonymous
  • anonymous
Yes please,
anonymous
  • anonymous
the whole thing and if i have a question can i ask?
anonymous
  • anonymous
then how come u are solving such a problem when u need the fundamentals?
anonymous
  • anonymous
I have rules here but im confused how i am apply to . I am able to solve the basic problems
anonymous
  • anonymous
i have test next week and I want to do good :(
anonymous
  • anonymous
please help me with this question.
anonymous
  • anonymous
I am and i will i promised
anonymous
  • anonymous
Thank you so much.
anonymous
  • anonymous
can u memorize the followings for me ...!
anonymous
  • anonymous
if u have u x v then when u want to differentiate it we use something called the product rule...
anonymous
  • anonymous
Ok thank you for the fact.
anonymous
  • anonymous
example :
anonymous
  • anonymous
if u= x^2 and v = e^x, and we were asked to find the derivative of(uv)
anonymous
  • anonymous
we apply this rule u v' + u' v
anonymous
  • anonymous
ok!
anonymous
  • anonymous
so what u do is u=x^2, u'=2x, v=e^x, u=e^x
anonymous
  • anonymous
now can u put the above in the following u v' + u' v
anonymous
  • anonymous
mm for my question?
anonymous
  • anonymous
no for my question
anonymous
  • anonymous
if u= x^2 and v = e^x, and we were asked to find the derivative of(uv) so what u do is u=x^2, u'=2x, v=e^x, u=e^x u v' + u' v
anonymous
  • anonymous
ok, x^2(e^x)+2x(ve^x)
anonymous
  • anonymous
well done but without the v
anonymous
  • anonymous
without v in the end?
anonymous
  • anonymous
look at what u wrote
anonymous
  • anonymous
yes,
anonymous
  • anonymous
what is the v doing in the equation and u got rid of it by subbing the functions in terms of x
anonymous
  • anonymous
Oh! sorry yes.
anonymous
  • anonymous
ok good now solve for ur question t3^t
anonymous
  • anonymous
how?
anonymous
  • anonymous
using the product rule then one u just solved above
anonymous
  • anonymous
so use the same steps i showed u
anonymous
  • anonymous
\[f(x)(2t^2+t3^t)(sqrtx)-(sqrtx)(2t^2+t3^t)\] from the producet rule?
anonymous
  • anonymous
no i said solve this one t2^t, please follow what i am asking u to do...not ur own rules or derrieres
anonymous
  • anonymous
but thats what i have told in the class something like that. or maybe I was wrong. could you show me everything and the answer?
anonymous
  • anonymous
right now, I am very confused. ;/ sorry
anonymous
  • anonymous
yes but don't forget we decided to break it a part then when we join everything together u'll see the final answer
anonymous
  • anonymous
O. I see sorry i was misleading
anonymous
  • anonymous
ok then lead now, so wat is diff of t3^t?
anonymous
  • anonymous
(t)(3^t)"+t?
anonymous
  • anonymous
use the u v' + u' v rule that i just showed u
anonymous
  • anonymous
(t)(3^t)+(3^t)(t)?
anonymous
  • anonymous
i just told u how to find u' of 3^t
anonymous
  • anonymous
i told u to memorize or take a not of it
anonymous
  • anonymous
\Large w=\frac{\sqrt{t}}{3^t t+2^2}
anonymous
  • anonymous
\[\Large w=\frac{\sqrt{t}}{3^t t+2^2}\]
anonymous
  • anonymous
this is ur equation right?
anonymous
  • anonymous
no.
anonymous
  • anonymous
its 2t^2+t3^t
anonymous
  • anonymous
oh ok
anonymous
  • anonymous
\[\Large w=\frac{\sqrt{t}}{3^t t+2t^2}\]
anonymous
  • anonymous
ok let's us apply the quotient rule
anonymous
  • anonymous
so let u =t^(1/2) and v=2t^2+t3^t, so what would u', and v' be?
anonymous
  • anonymous
or what would du=? and dv=?
anonymous
  • anonymous
uv'=vu"
anonymous
  • anonymous
(t^1/2)(2t^2+t3^t)+(2t^2+t3^t)
anonymous
  • anonymous
u = t^(1/2) that mean u'=(1/2)t^(-(1/2))
anonymous
  • anonymous
yes, i got it
anonymous
  • anonymous
ops sorry
anonymous
  • anonymous
good girl now tell me
anonymous
  • anonymous
if v=2t^2+t3^t what is v'?
anonymous
  • anonymous
how did you guess that i was a girl. 3^2in(3)?
anonymous
  • anonymous
why do u think i am wrong?
anonymous
  • anonymous
?
anonymous
  • anonymous
\[v=2t^2+t3^t \rightarrow v'=4t+3^t+t(3^tln(3))\]
anonymous
  • anonymous
are u there or surprise?
anonymous
  • anonymous
sorry i was looking above to recall again.
anonymous
  • anonymous
i told u to write
anonymous
  • anonymous
write on a piece of paper
anonymous
  • anonymous
I am.
anonymous
  • anonymous
\[\frac{g(x)f(x)'-f(x)g(x)'}{g(x)^2}\]
anonymous
  • anonymous
yes,
anonymous
  • anonymous
\[g(x)=\sqrt{t} \space and \space f(x)=2t^2+t3^t\]
anonymous
  • anonymous
plug into the equation right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
but f'(x) and g"(x) needs to be calculated differently
anonymous
  • anonymous
yes
anonymous
  • anonymous
g(x) =t^(1/2), what is g'(x)?
anonymous
  • anonymous
1/2t^-(1/2)
anonymous
  • anonymous
how?
anonymous
  • anonymous
nope try again
anonymous
  • anonymous
recall \[nt^{(n-1)}\]
anonymous
  • anonymous
hint n=(1/2)
anonymous
  • anonymous
r u there?
anonymous
  • anonymous
(1/2) t^-(1/2)
anonymous
  • anonymous
well done
anonymous
  • anonymous
if u solve this one the ur almost done with the question
anonymous
  • anonymous
\[ f(t)=2t^2+t3^t \space f'(t)?\]
anonymous
  • anonymous
are u there?
anonymous
  • anonymous
t3^t(in3)?
anonymous
  • anonymous
what happened to the 2t^2 and the product rule, if u look up i solved this for like 23084920384 times
anonymous
  • anonymous
4t+2^t+t3^t(In3)
anonymous
  • anonymous
good now plug the whole thing in the quotient rule
anonymous
  • anonymous
Oh I see thank you! i got it~
anonymous
  • anonymous
:)
anonymous
  • anonymous
ya but that is not the end
anonymous
  • anonymous
u still have more to the problem
anonymous
  • anonymous
sorry could you wait for 5 mins? im going back to my room and change to my comp?

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