Dodo1
Please help me math talent!



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TrashMan914
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If you say so.

Dodo1
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Thank you!

TrashMan914
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You're welcome.

Dodo1
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\[w=\frac{ \sqrt(x) }{ 2^2+t3^t } \]

Dodo1
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sorry it should be sart (t)

Dodo1
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and find dw/dt

mathsmind
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that is simple

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

mathsmind
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when u answer my question i sill proceed

TrashMan914
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Math, you can't simply give them the answer. It's against CoC. Guide them to it, so they can answer it themselves.

Dodo1
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step by step pleae!

Dodo1
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*please

.Sam.
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Quotient rule with respect to (t)..

Dodo1
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g(x)f(x)'f(x)g(x)'/g(x)^2

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

.Sam.
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You can use chain rule as well

Dodo1
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therefore, (2t62+t3^t)d/dx(sqrt(t)sqrt(t)(2t^2+t3^t)/(2t^2+t3^t)^2

.Sam.
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Followed by product rule

Dodo1
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I dont how how to caculate the root.

Dodo1
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and how to do (2t62+3t^3) to derivative?

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

Dodo1
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my teacher told me to do something like 1/2x^1/2? is it wrong

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

Dodo1
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no \[w=\frac{ Sqrt(t) }{ 2t^2+t3^t }\]

.Sam.
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You sure? the answer is \[\Large \frac{dw}{dt}=\frac{3^t+t \left(3^t (9 \log )+6\right)}{2 t^{3/2} \left(2 t+3^t\right)^2}\]

Dodo1
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no you dont use log. i have not learnt that yet

.Sam.
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\[\Large \frac{dw}{dt}=\frac{3^t+t \left(3^t ( \ln(9) )+6\right)}{2 t^{3/2} \left(2 t+3^t\right)^2}\]
This?

Dodo1
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mm maybe but is it possible to go simpler than this?

Dodo1
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is it not possible?

.Sam.
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no its not possible, other results are

Dodo1
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I only have learned power rule, exponential rule and product rule. ( chain rule)

mathsmind
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step one use the quotient rule..

mathsmind
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the only trick u have here is 3^t, u may use the table or Doperator...

Dodo1
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yes I did! its above. I dont know how to break down and power rules.

Dodo1
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please show me step by step.

mathsmind
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let me show u how to solve 3^t

mathsmind
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is that the part ur are struggling with right

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

Dodo1
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Yes :( t3^t

Dodo1
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thank you so much. I want to cry right now

mathsmind
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stop crying and fight for the answer

Dodo1
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ok, i wil! thanks

mathsmind
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trust me i will let u solve this problem

Dodo1
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you wont help me?

Dodo1
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so far i have got

mathsmind
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damn i wrote the answer on another post hehehe

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

Dodo1
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\[\frac{ (2t^2+t3^t)(\sqrt(x)'\sqrt(x)(2t^2+t3^t) }{ (2t^2+t3^t)^2 }\]

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

mathsmind
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now do u know how this happend

Dodo1
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but its t3^t?

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

mathsmind
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because with the t we will get into the product rule

Dodo1
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ok, I got it. i am taking note hold on

Dodo1
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du_3^t why its In(3)?

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

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

Dodo1
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mm im not sure, , negative numbers?

mathsmind
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ln(u) = ln(3^t)

mathsmind
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now do u know how to differentiate both sides?

Dodo1
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No I am not sure.

Dodo1
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mutiply?

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

mathsmind
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ln(u) = tln(3)

mathsmind
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did u see what happend to t?

Dodo1
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power of t went outside of 3 and In?

mathsmind
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yes this is a primitive ln rule

Dodo1
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Oh I see.

Dodo1
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Do i use this everytime i do product?

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

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

Dodo1
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ok, I got it.

mathsmind
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sorry power of a log

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

Dodo1
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power of a log, ok !

Dodo1
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mmm.. y=In/(x)?

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

Dodo1
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wow, thats new to me!

mathsmind
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this is basic differentiation of natural log

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

Dodo1
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tIn(3)/x

mathsmind
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ok let me make this even simple

mathsmind
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so u don't get confused

Dodo1
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thanks for taking your time.

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

mathsmind
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can u memorize this for now and take it for granted

Dodo1
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Ok,

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

mathsmind
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hint: a=3

Dodo1
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mmm.... 3^tIn(3)?

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

Dodo1
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Ok I will.

Dodo1
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whats the next step?

mathsmind
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sorry i was replying to another post on set theory ok

Dodo1
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its okay.

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

Dodo1
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you mean 2t^2?

Dodo1
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2^tIn(2)+3tIn(3)?

mathsmind
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no 2^2 is a constant

mathsmind
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look at it again

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

mathsmind
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\[2^2+t3^t\]

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

Dodo1
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Oh! so its (4t)?

mathsmind
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ok listen let me solve it

mathsmind
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can u see how this happened?

mathsmind
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using the product rule

Dodo1
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No, wheres 2 go? theres no 2 in the answer

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

mathsmind
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listen y=4, what is y'?

Dodo1
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y=4?

Dodo1
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zero? beacuse its constant

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

Dodo1
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zero?

mathsmind
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yes well done

mathsmind
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so differentiate now t3^t

Dodo1
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3^3In(t)?

Dodo1
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no its 3 ^tIn(3)?

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

mathsmind
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do u know the product rule?

Dodo1
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I am not sure

mathsmind
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uv'+u'v???

mathsmind
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do u know that rule?

Dodo1
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yes I do qutiotinent rule?

mathsmind
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no i said product rule..

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

Dodo1
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sorry no.

Dodo1
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Yes please,

Dodo1
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the whole thing and if i have a question can i ask?

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

Dodo1
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I have rules here but im confused how i am apply to . I am able to solve the basic problems

Dodo1
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i have test next week and I want to do good :(

Dodo1
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please help me with this question.

mathsmind
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I am and i will i promised

Dodo1
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Thank you so much.

mathsmind
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can u memorize the followings for me ...!

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

Dodo1
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Ok thank you for the fact.

mathsmind
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example :

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

mathsmind
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we apply this rule u v' + u' v

Dodo1
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ok!

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

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

Dodo1
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mm for my question?

mathsmind
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no for my question

mathsmind
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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

Dodo1
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ok, x^2(e^x)+2x(ve^x)

mathsmind
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well done but without the v

Dodo1
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without v in the end?

mathsmind
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look at what u wrote

Dodo1
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yes,

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

Dodo1
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Oh! sorry yes.

mathsmind
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ok good now solve for ur question t3^t

Dodo1
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how?

mathsmind
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using the product rule then one u just solved above

mathsmind
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so use the same steps i showed u

Dodo1
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\[f(x)(2t^2+t3^t)(sqrtx)(sqrtx)(2t^2+t3^t)\] from the producet rule?

mathsmind
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no i said solve this one t2^t, please follow what i am asking u to do...not ur own rules or derrieres

Dodo1
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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?

Dodo1
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right now, I am very confused. ;/ sorry

mathsmind
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yes but don't forget we decided to break it a part then when we join everything together u'll see the final answer

Dodo1
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O. I see sorry i was misleading

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

Dodo1
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(t)(3^t)"+t?

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

Dodo1
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(t)(3^t)+(3^t)(t)?

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

mathsmind
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i told u to memorize or take a not of it

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

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

mathsmind
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this is ur equation right?

Dodo1
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no.

Dodo1
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its 2t^2+t3^t

mathsmind
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oh ok

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

mathsmind
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ok let's us apply the quotient rule

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

mathsmind
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or what would du=? and dv=?

Dodo1
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uv'=vu"

Dodo1
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(t^1/2)(2t^2+t3^t)+(2t^2+t3^t)

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

Dodo1
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yes, i got it

Dodo1
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ops sorry

mathsmind
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good girl now tell me

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

Dodo1
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how did you guess that i was a girl.
3^2in(3)?

mathsmind
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why do u think i am wrong?

Dodo1
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?

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

mathsmind
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are u there or surprise?

Dodo1
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sorry i was looking above to recall again.

mathsmind
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i told u to write

mathsmind
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write on a piece of paper

Dodo1
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I am.

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

Dodo1
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yes,

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

Dodo1
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plug into the equation right?

mathsmind
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yes

Dodo1
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but f'(x) and g"(x) needs to be calculated differently

mathsmind
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yes

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

Dodo1
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1/2t^(1/2)

mathsmind
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how?

mathsmind
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nope try again

mathsmind
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recall
\[nt^{(n1)}\]

mathsmind
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hint n=(1/2)

mathsmind
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r u there?

Dodo1
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(1/2) t^(1/2)

mathsmind
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well done

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

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

mathsmind
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are u there?

Dodo1
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t3^t(in3)?

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

Dodo1
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4t+2^t+t3^t(In3)

mathsmind
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good now plug the whole thing in the quotient rule

Dodo1
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Oh I see thank you! i got it~

Dodo1
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:)

mathsmind
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ya but that is not the end

mathsmind
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u still have more to the problem

Dodo1
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sorry could you wait for 5 mins?
im going back to my room and change to my comp?