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Dodo1

  • 2 years ago

Please help me math talent!

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  1. TrashMan914
    • 2 years ago
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    If you say so.

  2. Dodo1
    • 2 years ago
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    Thank you!

  3. TrashMan914
    • 2 years ago
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    You're welcome.

  4. Dodo1
    • 2 years ago
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    \[w=\frac{ \sqrt(x) }{ 2^2+t3^t } \]

  5. Dodo1
    • 2 years ago
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    sorry it should be sart (t)

  6. Dodo1
    • 2 years ago
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    and find dw/dt

  7. mathsmind
    • 2 years ago
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    that is simple

  8. mathsmind
    • 2 years ago
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    do u want the answer or do u want a step by step solution?

  9. mathsmind
    • 2 years ago
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    when u answer my question i sill proceed

  10. TrashMan914
    • 2 years ago
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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.

  11. Dodo1
    • 2 years ago
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    step by step pleae!

  12. Dodo1
    • 2 years ago
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    *please

  13. .Sam.
    • 2 years ago
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    Quotient rule with respect to (t)..

  14. Dodo1
    • 2 years ago
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    g(x)f(x)'-f(x)g(x)'/g(x)^2

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

  16. .Sam.
    • 2 years ago
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    You can use chain rule as well

  17. Dodo1
    • 2 years ago
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    therefore, (2t62+t3^t)d/dx(sqrt(t)-sqrt(t)(2t^2+t3^t)/(2t^2+t3^t)^2

  18. .Sam.
    • 2 years ago
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    Followed by product rule

  19. Dodo1
    • 2 years ago
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    I dont how how to caculate the root.

  20. Dodo1
    • 2 years ago
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    and how to do (2t62+3t^3) to derivative?

  21. .Sam.
    • 2 years ago
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    The root "x" is just acted like constant, ignore it

  22. Dodo1
    • 2 years ago
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    my teacher told me to do something like 1/2x^-1/2? is it wrong

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

  24. Dodo1
    • 2 years ago
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    no \[w=\frac{ Sqrt(t) }{ 2t^2+t3^t }\]

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

  26. Dodo1
    • 2 years ago
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    no you dont use log. i have not learnt that yet

  27. .Sam.
    • 2 years ago
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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?

  28. Dodo1
    • 2 years ago
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    mm maybe but is it possible to go simpler than this?

  29. Dodo1
    • 2 years ago
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    is it not possible?

  30. .Sam.
    • 2 years ago
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    no its not possible, other results are

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  31. Dodo1
    • 2 years ago
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    I only have learned power rule, exponential rule and product rule. ( chain rule)

  32. mathsmind
    • 2 years ago
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    step one use the quotient rule..

  33. mathsmind
    • 2 years ago
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    the only trick u have here is 3^t, u may use the table or D-operator...

  34. Dodo1
    • 2 years ago
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    yes I did! its above. I dont know how to break down and power rules.

  35. Dodo1
    • 2 years ago
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    please show me step by step.

  36. mathsmind
    • 2 years ago
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    let me show u how to solve 3^t

  37. mathsmind
    • 2 years ago
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    is that the part ur are struggling with right

  38. mathsmind
    • 2 years ago
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    i will show u step by step but let's break this down

  39. Dodo1
    • 2 years ago
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    Yes :( t3^t

  40. Dodo1
    • 2 years ago
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    thank you so much. I want to cry right now

  41. mathsmind
    • 2 years ago
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    stop crying and fight for the answer

  42. Dodo1
    • 2 years ago
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    ok, i wil! thanks

  43. mathsmind
    • 2 years ago
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    trust me i will let u solve this problem

  44. Dodo1
    • 2 years ago
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    you wont help me?

  45. Dodo1
    • 2 years ago
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    so far i have got

  46. mathsmind
    • 2 years ago
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    damn i wrote the answer on another post hehehe

  47. mathsmind
    • 2 years ago
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    \[\[u = 3^t, \space du = 3^t \ln(3)\]\]

  48. Dodo1
    • 2 years ago
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    \[\frac{ (2t^2+t3^t)(\sqrt(x)'-\sqrt(x)(2t^2+t3^t) }{ (2t^2+t3^t)^2 }\]

  49. mathsmind
    • 2 years ago
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    \[u = 3^t, \space du = 3^t \ln(3)\]

  50. mathsmind
    • 2 years ago
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    now do u know how this happend

  51. Dodo1
    • 2 years ago
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    but its t3^t?

  52. mathsmind
    • 2 years ago
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    forget the t for now because i want to show u bit by bit

  53. mathsmind
    • 2 years ago
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    because with the t we will get into the product rule

  54. Dodo1
    • 2 years ago
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    ok, I got it. i am taking note hold on

  55. Dodo1
    • 2 years ago
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    du_3^t why its In(3)?

  56. mathsmind
    • 2 years ago
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    good question, now u r starting to listen and that is a good sign of learning...

  57. mathsmind
    • 2 years ago
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    u= 3^t what happens if you take the natural log of both sides?

  58. Dodo1
    • 2 years ago
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    mm im not sure, , negative numbers?

  59. mathsmind
    • 2 years ago
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    ln(u) = ln(3^t)

  60. mathsmind
    • 2 years ago
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    now do u know how to differentiate both sides?

  61. Dodo1
    • 2 years ago
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    No I am not sure.

  62. Dodo1
    • 2 years ago
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    mutiply?

  63. mathsmind
    • 2 years ago
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    ok no problem, first of all we need some log rules

  64. mathsmind
    • 2 years ago
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    ln(u) = tln(3)

  65. mathsmind
    • 2 years ago
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    did u see what happend to t?

  66. Dodo1
    • 2 years ago
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    power of t went outside of 3 and In?

  67. mathsmind
    • 2 years ago
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    yes this is a primitive ln rule

  68. Dodo1
    • 2 years ago
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    Oh I see.

  69. Dodo1
    • 2 years ago
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    Do i use this everytime i do product?

  70. mathsmind
    • 2 years ago
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    now if y=ln(x) what is y'?

  71. mathsmind
    • 2 years ago
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    u mean every time u have a log of a power?

  72. Dodo1
    • 2 years ago
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    ok, I got it.

  73. mathsmind
    • 2 years ago
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    sorry power of a log

  74. mathsmind
    • 2 years ago
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    now if y=ln(x) what is y'?

  75. Dodo1
    • 2 years ago
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    power of a log, ok !

  76. Dodo1
    • 2 years ago
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    mmm.. y=In/(x)?

  77. mathsmind
    • 2 years ago
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    no y=ln(x) ->y'=1/x

  78. Dodo1
    • 2 years ago
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    wow, thats new to me!

  79. mathsmind
    • 2 years ago
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    this is basic differentiation of natural log

  80. mathsmind
    • 2 years ago
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    so now back to our question ln(u) = tln(3) differentiate both sides...

  81. Dodo1
    • 2 years ago
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    tIn(3)/x

  82. mathsmind
    • 2 years ago
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    ok let me make this even simple

  83. mathsmind
    • 2 years ago
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    so u don't get confused

  84. Dodo1
    • 2 years ago
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    thanks for taking your time.

  85. mathsmind
    • 2 years ago
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    \[\frac{d}{dt}a^t=a^tln(a)\]

  86. mathsmind
    • 2 years ago
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    can u memorize this for now and take it for granted

  87. Dodo1
    • 2 years ago
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    Ok,

  88. mathsmind
    • 2 years ago
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    ok use this formula and tell me what is 3^t?

  89. mathsmind
    • 2 years ago
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    hint: a=3

  90. Dodo1
    • 2 years ago
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    mmm.... 3^tIn(3)?

  91. mathsmind
    • 2 years ago
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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...

  92. Dodo1
    • 2 years ago
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    Ok I will.

  93. Dodo1
    • 2 years ago
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    whats the next step?

  94. mathsmind
    • 2 years ago
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    sorry i was replying to another post on set theory ok

  95. Dodo1
    • 2 years ago
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    its okay.

  96. mathsmind
    • 2 years ago
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    now tell me how would u differentiate? \[ 2^2+t3^t \]

  97. Dodo1
    • 2 years ago
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    you mean 2t^2?

  98. Dodo1
    • 2 years ago
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    2^tIn(2)+3tIn(3)?

  99. mathsmind
    • 2 years ago
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    no 2^2 is a constant

  100. mathsmind
    • 2 years ago
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    look at it again

  101. mathsmind
    • 2 years ago
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    trust me by solving this part we are more than half way of solving the problem

  102. mathsmind
    • 2 years ago
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    \[2^2+t3^t\]

  103. mathsmind
    • 2 years ago
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    2^2=4 so when u differentiate a constant u get zero right!?

  104. Dodo1
    • 2 years ago
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    Oh! so its (4t)?

  105. mathsmind
    • 2 years ago
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    ok listen let me solve it

  106. mathsmind
    • 2 years ago
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    can u see how this happened?

  107. mathsmind
    • 2 years ago
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    using the product rule

  108. Dodo1
    • 2 years ago
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    No, wheres 2 go? theres no 2 in the answer

  109. mathsmind
    • 2 years ago
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    \[u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt\]

  110. mathsmind
    • 2 years ago
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    listen y=4, what is y'?

  111. Dodo1
    • 2 years ago
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    y=-4?

  112. Dodo1
    • 2 years ago
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    zero? beacuse its constant

  113. mathsmind
    • 2 years ago
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    zero well done, so y=2^2, y'=?

  114. Dodo1
    • 2 years ago
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    zero?

  115. mathsmind
    • 2 years ago
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    yes well done

  116. mathsmind
    • 2 years ago
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    so differentiate now t3^t

  117. Dodo1
    • 2 years ago
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    3^3In(t)?

  118. Dodo1
    • 2 years ago
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    no its 3 ^tIn(3)?

  119. mathsmind
    • 2 years ago
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    \[u=2^2+t3^t \rightarrow du=(3^t+t3^tln3))dt\]

  120. mathsmind
    • 2 years ago
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    do u know the product rule?

  121. Dodo1
    • 2 years ago
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    I am not sure

  122. mathsmind
    • 2 years ago
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    uv'+u'v???

  123. mathsmind
    • 2 years ago
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    do u know that rule?

  124. Dodo1
    • 2 years ago
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    yes I do qutiotinent rule?

  125. mathsmind
    • 2 years ago
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    no i said product rule..

  126. mathsmind
    • 2 years ago
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    do u want me to solve the whole thing then u may go and think about it?

  127. Dodo1
    • 2 years ago
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    sorry no.

  128. Dodo1
    • 2 years ago
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    Yes please,

  129. Dodo1
    • 2 years ago
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    the whole thing and if i have a question can i ask?

  130. mathsmind
    • 2 years ago
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    then how come u are solving such a problem when u need the fundamentals?

  131. Dodo1
    • 2 years ago
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    I have rules here but im confused how i am apply to . I am able to solve the basic problems

  132. Dodo1
    • 2 years ago
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    i have test next week and I want to do good :(

  133. Dodo1
    • 2 years ago
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    please help me with this question.

  134. mathsmind
    • 2 years ago
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    I am and i will i promised

  135. Dodo1
    • 2 years ago
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    Thank you so much.

  136. mathsmind
    • 2 years ago
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    can u memorize the followings for me ...!

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

  138. Dodo1
    • 2 years ago
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    Ok thank you for the fact.

  139. mathsmind
    • 2 years ago
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    example :

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

  141. mathsmind
    • 2 years ago
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    we apply this rule u v' + u' v

  142. Dodo1
    • 2 years ago
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    ok!

  143. mathsmind
    • 2 years ago
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    so what u do is u=x^2, u'=2x, v=e^x, u=e^x

  144. mathsmind
    • 2 years ago
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    now can u put the above in the following u v' + u' v

  145. Dodo1
    • 2 years ago
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    mm for my question?

  146. mathsmind
    • 2 years ago
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    no for my question

  147. mathsmind
    • 2 years ago
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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

  148. Dodo1
    • 2 years ago
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    ok, x^2(e^x)+2x(ve^x)

  149. mathsmind
    • 2 years ago
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    well done but without the v

  150. Dodo1
    • 2 years ago
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    without v in the end?

  151. mathsmind
    • 2 years ago
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    look at what u wrote

  152. Dodo1
    • 2 years ago
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    yes,

  153. mathsmind
    • 2 years ago
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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

  154. Dodo1
    • 2 years ago
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    Oh! sorry yes.

  155. mathsmind
    • 2 years ago
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    ok good now solve for ur question t3^t

  156. Dodo1
    • 2 years ago
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    how?

  157. mathsmind
    • 2 years ago
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    using the product rule then one u just solved above

  158. mathsmind
    • 2 years ago
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    so use the same steps i showed u

  159. Dodo1
    • 2 years ago
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    \[f(x)(2t^2+t3^t)(sqrtx)-(sqrtx)(2t^2+t3^t)\] from the producet rule?

  160. mathsmind
    • 2 years ago
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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

  161. Dodo1
    • 2 years ago
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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?

  162. Dodo1
    • 2 years ago
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    right now, I am very confused. ;/ sorry

  163. mathsmind
    • 2 years ago
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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

  164. Dodo1
    • 2 years ago
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    O. I see sorry i was misleading

  165. mathsmind
    • 2 years ago
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    ok then lead now, so wat is diff of t3^t?

  166. Dodo1
    • 2 years ago
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    (t)(3^t)"+t?

  167. mathsmind
    • 2 years ago
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    use the u v' + u' v rule that i just showed u

  168. Dodo1
    • 2 years ago
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    (t)(3^t)+(3^t)(t)?

  169. mathsmind
    • 2 years ago
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    i just told u how to find u' of 3^t

  170. mathsmind
    • 2 years ago
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    i told u to memorize or take a not of it

  171. mathsmind
    • 2 years ago
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    \Large w=\frac{\sqrt{t}}{3^t t+2^2}

  172. mathsmind
    • 2 years ago
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    \[\Large w=\frac{\sqrt{t}}{3^t t+2^2}\]

  173. mathsmind
    • 2 years ago
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    this is ur equation right?

  174. Dodo1
    • 2 years ago
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    no.

  175. Dodo1
    • 2 years ago
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    its 2t^2+t3^t

  176. mathsmind
    • 2 years ago
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    oh ok

  177. mathsmind
    • 2 years ago
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    \[\Large w=\frac{\sqrt{t}}{3^t t+2t^2}\]

  178. mathsmind
    • 2 years ago
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    ok let's us apply the quotient rule

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

  180. mathsmind
    • 2 years ago
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    or what would du=? and dv=?

  181. Dodo1
    • 2 years ago
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    uv'=vu"

  182. Dodo1
    • 2 years ago
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    (t^1/2)(2t^2+t3^t)+(2t^2+t3^t)

  183. mathsmind
    • 2 years ago
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    u = t^(1/2) that mean u'=(1/2)t^(-(1/2))

  184. Dodo1
    • 2 years ago
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    yes, i got it

  185. Dodo1
    • 2 years ago
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    ops sorry

  186. mathsmind
    • 2 years ago
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    good girl now tell me

  187. mathsmind
    • 2 years ago
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    if v=2t^2+t3^t what is v'?

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

  189. mathsmind
    • 2 years ago
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    why do u think i am wrong?

  190. Dodo1
    • 2 years ago
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    ?

  191. mathsmind
    • 2 years ago
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    \[v=2t^2+t3^t \rightarrow v'=4t+3^t+t(3^tln(3))\]

  192. mathsmind
    • 2 years ago
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    are u there or surprise?

  193. Dodo1
    • 2 years ago
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    sorry i was looking above to recall again.

  194. mathsmind
    • 2 years ago
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    i told u to write

  195. mathsmind
    • 2 years ago
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    write on a piece of paper

  196. Dodo1
    • 2 years ago
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    I am.

  197. mathsmind
    • 2 years ago
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    \[\frac{g(x)f(x)'-f(x)g(x)'}{g(x)^2}\]

  198. Dodo1
    • 2 years ago
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    yes,

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

  200. Dodo1
    • 2 years ago
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    plug into the equation right?

  201. mathsmind
    • 2 years ago
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    yes

  202. Dodo1
    • 2 years ago
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    but f'(x) and g"(x) needs to be calculated differently

  203. mathsmind
    • 2 years ago
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    yes

  204. mathsmind
    • 2 years ago
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    g(x) =t^(1/2), what is g'(x)?

  205. Dodo1
    • 2 years ago
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    1/2t^-(1/2)

  206. mathsmind
    • 2 years ago
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    how?

  207. mathsmind
    • 2 years ago
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    nope try again

  208. mathsmind
    • 2 years ago
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    recall \[nt^{(n-1)}\]

  209. mathsmind
    • 2 years ago
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    hint n=(1/2)

  210. mathsmind
    • 2 years ago
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    r u there?

  211. Dodo1
    • 2 years ago
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    (1/2) t^-(1/2)

  212. mathsmind
    • 2 years ago
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    well done

  213. mathsmind
    • 2 years ago
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    if u solve this one the ur almost done with the question

  214. mathsmind
    • 2 years ago
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    \[ f(t)=2t^2+t3^t \space f'(t)?\]

  215. mathsmind
    • 2 years ago
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    are u there?

  216. Dodo1
    • 2 years ago
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    t3^t(in3)?

  217. mathsmind
    • 2 years ago
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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

  218. Dodo1
    • 2 years ago
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    4t+2^t+t3^t(In3)

  219. mathsmind
    • 2 years ago
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    good now plug the whole thing in the quotient rule

  220. Dodo1
    • 2 years ago
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    Oh I see thank you! i got it~

  221. Dodo1
    • 2 years ago
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    :)

  222. mathsmind
    • 2 years ago
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    ya but that is not the end

  223. mathsmind
    • 2 years ago
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    u still have more to the problem

  224. Dodo1
    • 2 years ago
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    sorry could you wait for 5 mins? im going back to my room and change to my comp?

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