Please help me math talent!

- anonymous

Please help me math talent!

- Stacey Warren - Expert brainly.com

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- anonymous

If you say so.

- anonymous

Thank you!

- anonymous

You're welcome.

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## More answers

- anonymous

\[w=\frac{ \sqrt(x) }{ 2^2+t3^t } \]

- anonymous

sorry it should be sart (t)

- anonymous

and find dw/dt

- anonymous

that is simple

- anonymous

do u want the answer or do u want a step by step solution?

- anonymous

when u answer my question i sill proceed

- 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

step by step pleae!

- anonymous

*please

- .Sam.

Quotient rule with respect to (t)..

- anonymous

g(x)f(x)'-f(x)g(x)'/g(x)^2

- .Sam.

This right\[w=\frac{\sqrt{x}}{3^t t+2^2}\]

- .Sam.

You can use chain rule as well

- anonymous

therefore, (2t62+t3^t)d/dx(sqrt(t)-sqrt(t)(2t^2+t3^t)/(2t^2+t3^t)^2

- .Sam.

Followed by product rule

- anonymous

I dont how how to caculate the root.

- anonymous

and how to do (2t62+3t^3) to derivative?

- .Sam.

The root "x" is just acted like constant, ignore it

- anonymous

my teacher told me to do something like 1/2x^-1/2? is it wrong

- .Sam.

is the question this?\[\Large w=\frac{\sqrt{x}}{3^t t+2^2}\]

- anonymous

no \[w=\frac{ Sqrt(t) }{ 2t^2+t3^t }\]

- .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

no you dont use log. i have not learnt that yet

- .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

mm maybe but is it possible to go simpler than this?

- anonymous

is it not possible?

- .Sam.

no its not possible, other results are

##### 1 Attachment

- anonymous

I only have learned power rule, exponential rule and product rule. ( chain rule)

- anonymous

step one use the quotient rule..

- anonymous

the only trick u have here is 3^t, u may use the table or D-operator...

- anonymous

yes I did! its above. I dont know how to break down and power rules.

- anonymous

please show me step by step.

- anonymous

let me show u how to solve 3^t

- anonymous

is that the part ur are struggling with right

- anonymous

i will show u step by step but let's break this down

- anonymous

Yes :( t3^t

- anonymous

thank you so much. I want to cry right now

- anonymous

stop crying and fight for the answer

- anonymous

ok, i wil! thanks

- anonymous

trust me i will let u solve this problem

- anonymous

you wont help me?

- anonymous

so far i have got

- anonymous

damn i wrote the answer on another post hehehe

- anonymous

\[\[u = 3^t, \space du = 3^t \ln(3)\]\]

- anonymous

\[\frac{ (2t^2+t3^t)(\sqrt(x)'-\sqrt(x)(2t^2+t3^t) }{ (2t^2+t3^t)^2 }\]

- anonymous

\[u = 3^t, \space du = 3^t \ln(3)\]

- anonymous

now do u know how this happend

- anonymous

but its t3^t?

- anonymous

forget the t for now because i want to show u bit by bit

- anonymous

because with the t we will get into the product rule

- anonymous

ok, I got it. i am taking note hold on

- anonymous

du_3^t why its In(3)?

- anonymous

good question, now u r starting to listen and that is a good sign of learning...

- anonymous

u= 3^t what happens if you take the natural log of both sides?

- anonymous

mm im not sure, , negative numbers?

- anonymous

ln(u) = ln(3^t)

- anonymous

now do u know how to differentiate both sides?

- anonymous

No I am not sure.

- anonymous

mutiply?

- anonymous

ok no problem, first of all we need some log rules

- anonymous

ln(u) = tln(3)

- anonymous

did u see what happend to t?

- anonymous

power of t went outside of 3 and In?

- anonymous

yes this is a primitive ln rule

- anonymous

Oh I see.

- anonymous

Do i use this everytime i do product?

- anonymous

now if y=ln(x) what is y'?

- anonymous

u mean every time u have a log of a power?

- anonymous

ok, I got it.

- anonymous

sorry power of a log

- anonymous

now if y=ln(x) what is y'?

- anonymous

power of a log, ok !

- anonymous

mmm.. y=In/(x)?

- anonymous

no y=ln(x) ->y'=1/x

- anonymous

wow, thats new to me!

- anonymous

this is basic differentiation of natural log

- anonymous

so now back to our question ln(u) = tln(3) differentiate both sides...

- anonymous

tIn(3)/x

- anonymous

ok let me make this even simple

- anonymous

so u don't get confused

- anonymous

thanks for taking your time.

- anonymous

\[\frac{d}{dt}a^t=a^tln(a)\]

- anonymous

can u memorize this for now and take it for granted

- anonymous

Ok,

- anonymous

ok use this formula and tell me what is 3^t?

- anonymous

hint: a=3

- anonymous

mmm.... 3^tIn(3)?

- anonymous

well done so memorize that please take a note and keep it in ur mind the same way u know ur name...

- anonymous

Ok I will.

- anonymous

whats the next step?

- anonymous

sorry i was replying to another post on set theory ok

- anonymous

its okay.

- anonymous

now tell me how would u differentiate? \[ 2^2+t3^t \]

- anonymous

you mean 2t^2?

- anonymous

2^tIn(2)+3tIn(3)?

- anonymous

no 2^2 is a constant

- anonymous

look at it again

- anonymous

trust me by solving this part we are more than half way of solving the problem

- anonymous

\[2^2+t3^t\]

- anonymous

2^2=4 so when u differentiate a constant u get zero right!?

- anonymous

Oh! so its (4t)?

- anonymous

ok listen let me solve it

- anonymous

can u see how this happened?

- anonymous

using the product rule

- anonymous

No, wheres 2 go? theres no 2 in the answer

- anonymous

\[u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt\]

- anonymous

listen y=4, what is y'?

- anonymous

y=-4?

- anonymous

zero? beacuse its constant

- anonymous

zero well done, so y=2^2, y'=?

- anonymous

zero?

- anonymous

yes well done

- anonymous

so differentiate now t3^t

- anonymous

3^3In(t)?

- anonymous

no its 3 ^tIn(3)?

- anonymous

\[u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt\]

- anonymous

do u know the product rule?

- anonymous

I am not sure

- anonymous

uv'+u'v???

- anonymous

do u know that rule?

- anonymous

yes I do qutiotinent rule?

- anonymous

no i said product rule..

- anonymous

do u want me to solve the whole thing then u may go and think about it?

- anonymous

sorry no.

- anonymous

Yes please,

- anonymous

the whole thing and if i have a question can i ask?

- anonymous

then how come u are solving such a problem when u need the fundamentals?

- anonymous

I have rules here but im confused how i am apply to . I am able to solve the basic problems

- anonymous

i have test next week and I want to do good :(

- anonymous

please help me with this question.

- anonymous

I am and i will i promised

- anonymous

Thank you so much.

- anonymous

can u memorize the followings for me ...!

- anonymous

if u have u x v then when u want to differentiate it we use something called the product rule...

- anonymous

Ok thank you for the fact.

- anonymous

example :

- anonymous

if u= x^2 and v = e^x, and we were asked to find the derivative of(uv)

- anonymous

we apply this rule u v' + u' v

- anonymous

ok!

- anonymous

so what u do is u=x^2, u'=2x, v=e^x, u=e^x

- anonymous

now can u put the above in the following u v' + u' v

- anonymous

mm for my question?

- anonymous

no for my question

- 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

ok, x^2(e^x)+2x(ve^x)

- anonymous

well done but without the v

- anonymous

without v in the end?

- anonymous

look at what u wrote

- anonymous

yes,

- anonymous

what is the v doing in the equation and u got rid of it by subbing the functions in terms of x

- anonymous

Oh! sorry yes.

- anonymous

ok good now solve for ur question t3^t

- anonymous

how?

- anonymous

using the product rule then one u just solved above

- anonymous

so use the same steps i showed u

- anonymous

\[f(x)(2t^2+t3^t)(sqrtx)-(sqrtx)(2t^2+t3^t)\] from the producet rule?

- 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

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

right now, I am very confused. ;/ sorry

- 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

O. I see sorry i was misleading

- anonymous

ok then lead now, so wat is diff of t3^t?

- anonymous

(t)(3^t)"+t?

- anonymous

use the u v' + u' v rule that i just showed u

- anonymous

(t)(3^t)+(3^t)(t)?

- anonymous

i just told u how to find u' of 3^t

- anonymous

i told u to memorize or take a not of it

- anonymous

\Large w=\frac{\sqrt{t}}{3^t t+2^2}

- anonymous

\[\Large w=\frac{\sqrt{t}}{3^t t+2^2}\]

- anonymous

this is ur equation right?

- anonymous

no.

- anonymous

its 2t^2+t3^t

- anonymous

oh ok

- anonymous

\[\Large w=\frac{\sqrt{t}}{3^t t+2t^2}\]

- anonymous

ok let's us apply the quotient rule

- anonymous

so let u =t^(1/2) and v=2t^2+t3^t, so what would u', and v' be?

- anonymous

or what would du=? and dv=?

- anonymous

uv'=vu"

- anonymous

(t^1/2)(2t^2+t3^t)+(2t^2+t3^t)

- anonymous

u = t^(1/2) that mean u'=(1/2)t^(-(1/2))

- anonymous

yes, i got it

- anonymous

ops sorry

- anonymous

good girl now tell me

- anonymous

if v=2t^2+t3^t what is v'?

- anonymous

how did you guess that i was a girl. 3^2in(3)?

- anonymous

why do u think i am wrong?

- anonymous

?

- anonymous

\[v=2t^2+t3^t \rightarrow v'=4t+3^t+t(3^tln(3))\]

- anonymous

are u there or surprise?

- anonymous

sorry i was looking above to recall again.

- anonymous

i told u to write

- anonymous

write on a piece of paper

- anonymous

I am.

- anonymous

\[\frac{g(x)f(x)'-f(x)g(x)'}{g(x)^2}\]

- anonymous

yes,

- anonymous

\[g(x)=\sqrt{t} \space and \space f(x)=2t^2+t3^t\]

- anonymous

plug into the equation right?

- anonymous

yes

- anonymous

but f'(x) and g"(x) needs to be calculated differently

- anonymous

yes

- anonymous

g(x) =t^(1/2), what is g'(x)?

- anonymous

1/2t^-(1/2)

- anonymous

how?

- anonymous

nope try again

- anonymous

recall \[nt^{(n-1)}\]

- anonymous

hint n=(1/2)

- anonymous

r u there?

- anonymous

(1/2) t^-(1/2)

- anonymous

well done

- anonymous

if u solve this one the ur almost done with the question

- anonymous

\[ f(t)=2t^2+t3^t \space f'(t)?\]

- anonymous

are u there?

- anonymous

t3^t(in3)?

- anonymous

what happened to the 2t^2 and the product rule, if u look up i solved this for like 23084920384 times

- anonymous

4t+2^t+t3^t(In3)

- anonymous

good now plug the whole thing in the quotient rule

- anonymous

Oh I see thank you! i got it~

- anonymous

:)

- anonymous

ya but that is not the end

- anonymous

u still have more to the problem

- anonymous

sorry could you wait for 5 mins? im going back to my room and change to my comp?

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