Question

Please help me math talent!

Answer 1

If you say so.

Answer 2

Thank you!

Answer 3

You're welcome.

Answer 4

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

Answer 5

sorry it should be sart (t)

Answer 6

and find dw/dt

Answer 7

that is simple

Answer 8

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

Answer 9

when u answer my question i sill proceed

Answer 10

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

Answer 11

step by step pleae!

Answer 12

*please

Answer 13

Quotient rule with respect to (t)..

Answer 14

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

Answer 15

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

Answer 16

You can use chain rule as well

Answer 17

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

Answer 18

Followed by product rule

Answer 19

I dont how how to caculate the root.

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

is it not possible?

Answer 30

no its not possible, other results are

Answer 31

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

Answer 32

step one use the quotient rule..

Answer 33

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

Answer 34

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

Answer 35

please show me step by step.

Answer 36

let me show u how to solve 3^t

Answer 37

is that the part ur are struggling with right

Answer 38

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

Answer 39

Yes :( t3^t

Answer 40

thank you so much. I want to cry right now

Answer 41

stop crying and fight for the answer

Answer 42

ok, i wil! thanks

Answer 43

trust me i will let u solve this problem

Answer 44

you wont help me?

Answer 45

so far i have got

Answer 46

damn i wrote the answer on another post hehehe

Answer 47

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

Answer 48

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

Answer 49

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

Answer 50

now do u know how this happend

Answer 51

but its t3^t?

Answer 52

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

Answer 53

because with the t we will get into the product rule

Answer 54

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

Answer 55

du_3^t why its In(3)?

Answer 56

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

Answer 57

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

Answer 58

mm im not sure, , negative numbers?

Answer 59

ln(u) = ln(3^t)

Answer 60

now do u know how to differentiate both sides?

Answer 61

No I am not sure.

Answer 62

mutiply?

Answer 63

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

Answer 64

ln(u) = tln(3)

Answer 65

did u see what happend to t?

Answer 66

power of t went outside of 3 and In?

Answer 67

yes this is a primitive ln rule

Answer 68

Oh I see.

Answer 69

Do i use this everytime i do product?

Answer 70

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

Answer 71

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

Answer 72

ok, I got it.

Answer 73

sorry power of a log

Answer 74

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

Answer 75

power of a log, ok !

Answer 76

mmm.. y=In/(x)?

Answer 77

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

Answer 78

wow, thats new to me!

Answer 79

this is basic differentiation of natural log

Answer 80

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

Answer 81

tIn(3)/x

Answer 82

ok let me make this even simple

Answer 83

so u don't get confused

Answer 84

thanks for taking your time.

Answer 85

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

Answer 86

can u memorize this for now and take it for granted

Answer 87

Ok,

Answer 88

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

Answer 89

hint: a=3

Answer 90

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

Answer 91

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

Answer 92

Ok I will.

Answer 93

whats the next step?

Answer 94

sorry i was replying to another post on set theory ok

Answer 95

its okay.

Answer 96

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

Answer 97

you mean 2t^2?