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anonymous

  • 5 years ago

find the derivative of y = sqrt(3)+(x)^1/3 + 1/x???

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  1. anonymous
    • 5 years ago
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    \[\sqrt{x}+x^{\frac{1}{3}}+\frac{1}{x}\]?

  2. anonymous
    • 5 years ago
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    so the problem is A) \[y=\sqrt{3+x ^{1/3}+1/x}\] or B) \[y=\sqrt{3}+x ^{1/3}+1/x\]

  3. anonymous
    • 5 years ago
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    or is first term \[\sqrt{3}\]?

  4. anonymous
    • 5 years ago
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    the b) style

  5. anonymous
    • 5 years ago
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    then do not be hoodwinked. \[\sqrt{3}\] is constant, its derivative is 0

  6. anonymous
    • 5 years ago
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    yeap derivative of a constant is zero

  7. anonymous
    • 5 years ago
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    satelllite ur dis ans is wrong it does not tally wid de book pls explain in detail

  8. anonymous
    • 5 years ago
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    oh i did not give a complete answer. sorry. i only said derivative of \[\sqrt{3}\] is 0 the others need power rule.

  9. anonymous
    • 5 years ago
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    (1/3)x^-2/3-1x^-2

  10. anonymous
    • 5 years ago
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    however, \[\frac{1}{x}\] os a very common function, so you should just remember its derivative without using power rule. the derivative of \[\frac{1}{x}\] is \[-\frac{1}{x^2}\]

  11. anonymous
    • 5 years ago
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    pls don't be angry at me cause i am in 11th and just a learner!!!!!!

  12. anonymous
    • 5 years ago
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    Guys I don't know how to write the equation here coz I am bad at latex stuffs

  13. anonymous
    • 5 years ago
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    k i will telll wat ans de book has

  14. anonymous
    • 5 years ago
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    comes up so often you do not want to compute it afresh each time. for \[x^{\frac{1}{3}}\] youi use the power rule to get \[\frac{1}{3}x^{-\frac{2}{3}}\]

  15. anonymous
    • 5 years ago
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    I hope tejeshwar95 got the answer

  16. anonymous
    • 5 years ago
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    it says - 1/2*sqrt(3/x)+1/3*1/x^(2/3) - 1/x^2

  17. anonymous
    • 5 years ago
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    which is the same as \[\frac{1}{2 \sqrt [3]{x^2}}\]

  18. anonymous
    • 5 years ago
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    can't understand a thing

  19. anonymous
    • 5 years ago
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    sorry lets go slow. is the first term just \[\sqrt{3}\] or is it \[\sqrt{3x}\]

  20. anonymous
    • 5 years ago
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    sorry for such a rude reply but i really can't get a hang of it!!!!! its sqrt(3x)

  21. anonymous
    • 5 years ago
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    ooooh then i apologize. i thought it was just \[\sqrt{3}\]

  22. anonymous
    • 5 years ago
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    its ok!!!!!!!!!!

  23. anonymous
    • 5 years ago
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    lets do them one at a time. you want to use the power rule, which says that the derivative of \[x^r\] is \[r\times x^{r-1}\] ok so far?

  24. anonymous
    • 5 years ago
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    wat is de power rule??? haven't heard bout it

  25. anonymous
    • 5 years ago
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    it tells you how to find the derivative of something raised to a power. for example the derivative of \[x^3\] is \[3x^2\]

  26. anonymous
    • 5 years ago
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    ok?

  27. anonymous
    • 5 years ago
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    ok the 1 which says if y = x^n then n(x)^n-1

  28. anonymous
    • 5 years ago
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    yups got it till here!!!!!!

  29. anonymous
    • 5 years ago
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    yes that is the power rule.

  30. anonymous
    • 5 years ago
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    so the trick is to write each of these terms in terms of exponents and then use the power rule.

  31. anonymous
    • 5 years ago
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    k let me try it on paper hang on for a minute!!!!!!

  32. anonymous
    • 5 years ago
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    now \[x^{\frac{1}{3}}\] is already written that way so that one is easy.

  33. anonymous
    • 5 years ago
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    i will wait.

  34. anonymous
    • 5 years ago
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    as far as \[\sqrt{3}\] isconcerned we remove the 3??? cause we can't differentiate it???

  35. anonymous
    • 5 years ago
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    this one is the confusing one, but don't be fooled. \[\sqrt{3x}=\sqrt{3} \times \sqrt{x} = \sqrt{3}\times {x^{\frac{1}{2}}}\] and a constant just stays there.

  36. anonymous
    • 5 years ago
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    k got it till here

  37. anonymous
    • 5 years ago
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    for example, the derivative of \[x^2 \] is \[2x\] and the derivative of \[\sqrt{3}x^2\] is \[2 \sqrt{3}x\] the constant just says as a multiplier, so ignore it.

  38. anonymous
    • 5 years ago
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    k so i ignore sqrt(3)

  39. anonymous
    • 5 years ago
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    so only use the power rule on the \[x^\frac{1}{2}\] part. bring out the exponent as a multiplier, and then subtract 1 from the exponent. i wait while you try it.

  40. anonymous
    • 5 years ago
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    but now did u take \[\sqrt{3}x ^{2}\] come into picture

  41. anonymous
    • 5 years ago
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    u took it as an eg???

  42. anonymous
    • 5 years ago
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    that was just an example to explain that the \[\sqrt{3}\] is unimportant. just a side example. not part of this problem.

  43. anonymous
    • 5 years ago
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    yes just eg.

  44. anonymous
    • 5 years ago
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    k now after trying i got 1/2*x ^-1/2

  45. anonymous
    • 5 years ago
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    yes!

  46. anonymous
    • 5 years ago
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    now convert back to radical from from exponential form.

  47. anonymous
    • 5 years ago
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    k correct till here sorry for being so slow

  48. anonymous
    • 5 years ago
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    no problems. long as you understand.

  49. anonymous
    • 5 years ago
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    do the same again??????

  50. anonymous
    • 5 years ago
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    do you know what \[x^{-\frac{1}{2}}\] is in radical form?

  51. anonymous
    • 5 years ago
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    if not i explain, if so just convert back.

  52. anonymous
    • 5 years ago
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    nope not exactly

  53. anonymous
    • 5 years ago
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    ok. i explain. the exponent has a minus sign, so that means take the reciprocal. for example, \[x^{-5}=\frac{1}{x^5}\]

  54. anonymous
    • 5 years ago
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    yups got it

  55. anonymous
    • 5 years ago
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    the exponent is a fraction. the denominator is 2, so that means take the square root. the numerator is 1, so raise it to the power of 1, which is like doing nothing. so \[x^{-\frac{1}{2}}=\frac{1}{\sqrt{x}}\]

  56. anonymous
    • 5 years ago
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    therefore \[\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}\]

  57. anonymous
    • 5 years ago
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    so far so good?

  58. anonymous
    • 5 years ago
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    so we put \[\sqrt{x^3}\] or \[\sqrt{x}\]

  59. anonymous
    • 5 years ago
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    in the denominator!!!!!!

  60. anonymous
    • 5 years ago
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    just \[\sqrt{x}\] in the denominator. but also a 2 in the denominator because you are multiplying by 1/2

  61. anonymous
    • 5 years ago
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    and the numerator is this case is \[\sqrt{3}\] because that constant is still there.

  62. anonymous
    • 5 years ago
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    can we have a voice chat???? dis is becoming a pain!!!!!!

  63. anonymous
    • 5 years ago
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    final answer: \[\frac{\sqrt{3}}{2\sqrt{x}}\]

  64. anonymous
    • 5 years ago
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    don't know how to voice chat. do you?

  65. anonymous
    • 5 years ago
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    nope

  66. anonymous
    • 5 years ago
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    voltage drops are happening i might not reply in between

  67. anonymous
    • 5 years ago
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    ok. the reason this problem is a pain for you is that you have to do three things: 1)convert to exponential form 2) use the power rule 3) convert back to radical form

  68. anonymous
    • 5 years ago
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    if u can hang around then give me some time i will just go through dese rules!!!!!!!!

  69. anonymous
    • 5 years ago
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    but you probably know what \[7\times 8\] is because you have it memorized. since you are taking calculus, and since \[\sqrt{x}\] is such a common function, you should probably memorize its derivative, which is \[\frac{1}{2\sqrt{x}}\] that way you never have to do this again!

  70. anonymous
    • 5 years ago
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    saves you the three steps of writing in exponential form, using the power rule, and converting back. if you remember it then for homework or on a test you just write it.

  71. anonymous
    • 5 years ago
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    k learnt

  72. anonymous
    • 5 years ago
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    and derived

  73. anonymous
    • 5 years ago
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    and another very common function is \[f(x)=\frac{1}{x}\]

  74. anonymous
    • 5 years ago
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    its derivative is \[f'(x)=-\frac{1}{x^2}\]

  75. anonymous
    • 5 years ago
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    k got it

  76. anonymous
    • 5 years ago
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    but could not derive it!!!!!!!!

  77. anonymous
    • 5 years ago
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    note the "-" sign. you can do this using the power rule as well, but it never changes. \[\frac{1}{x}=x^{-1}\] power rule gives \[-1\times x^{-2}=-\frac{1}{x^2}\]

  78. anonymous
    • 5 years ago
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    when do u come online tomorrow i am tired i need to relax!!!!!!!!!!

  79. anonymous
    • 5 years ago
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    or give me ur no if u live in delhi den i can talk 2 u over de phone!!!!!!!

  80. anonymous
    • 5 years ago
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    probably in the morning if you are here then. review power rule and of course exponents (because that is what it uses) in the mean time. good luck!

  81. anonymous
    • 5 years ago
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    no i am in us.

  82. anonymous
    • 5 years ago
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    k so wat's de time dere now????????

  83. anonymous
    • 5 years ago
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    thanx for ur help and the pains u took but if u cud come online at the same time as u came 2day den it wud be gr8

  84. anonymous
    • 5 years ago
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    ok i will try. look for me around this time or a little earlier.

  85. anonymous
    • 5 years ago
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    like wat's de time in US?? then i can guess wen 2 come online!!!!!!

  86. anonymous
    • 5 years ago
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    or can u hang around for a while ny the time i play a bit of COD

  87. anonymous
    • 5 years ago
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    k luks like i got it!!!!!!!!!!!

  88. anonymous
    • 5 years ago
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    ok i will be here for a while. have some work to do.

  89. anonymous
    • 5 years ago
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    i got the simplified form but ain't getin de full ans!!!!!!!!!!!

  90. anonymous
    • 5 years ago
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    to part 1?

  91. anonymous
    • 5 years ago
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    I got till see attachment

  92. anonymous
    • 5 years ago
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    1 Attachment
  93. anonymous
    • 5 years ago
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    avoid the torn part look at the 1 written below!!!!!!!

  94. anonymous
    • 5 years ago
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    looks good to me. of course you still have actually subtract the exponents and convert back to radical form.

  95. anonymous
    • 5 years ago
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    how do i do dat pls tell!!!!!!

  96. anonymous
    • 5 years ago
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    lets do the middle one. \[\frac{1}{3}x^{\frac{1}{3}-1}=\frac{1}{3}x^{-\frac{2}{3}}\]

  97. anonymous
    • 5 years ago
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    so far so good?

  98. anonymous
    • 5 years ago
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    \[\frac{1}{3}x^{-\frac{2}{3}}=\frac{1}{3\sqrt[3]{x^2}}\]

  99. anonymous
    • 5 years ago
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    yups

  100. anonymous
    • 5 years ago
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    last one: \[-1x^{-1-1}=-1x^{-2}=\frac{-1}{x^2}\]

  101. anonymous
    • 5 years ago
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    yups

  102. anonymous
    • 5 years ago
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    luks like i got the whole answer

  103. anonymous
    • 5 years ago
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    and first one: \[\sqrt{3}\frac{1}{2}x^{\frac{1}{2}-1}=\sqrt{3}\frac{1}{2}x^{-\frac{1}{2}}=\frac{\sqrt{3}}{2\sqrt{x}}\]

  104. anonymous
    • 5 years ago
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    ok?

  105. anonymous
    • 5 years ago
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    yups

  106. anonymous
    • 5 years ago
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    now try and easy one for yourself.

  107. anonymous
    • 5 years ago
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    dude can u pls give me ur email id so dat de next time i have a doubt i can send it across or even chat again DUDE U ROCK!!!!!!!!! THANX FOR DE PATIENCE, SUPPORT.

  108. anonymous
    • 5 years ago
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    no problem. you can email me here. best bet to catch me.

  109. anonymous
    • 5 years ago
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    hold on i send an email address.

  110. anonymous
    • 5 years ago
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    If u don't mind can u even give me ur landline or phone no my parents won't mind if i called some1 who can really help me through sticky situations!!!!!!!! and by the way a must watch!!!!! http://www.youtube.com/watch?v=kVFdAJRVm94

  111. anonymous
    • 5 years ago
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    and another vid which if u can understand the music's nice i couldn't understand!!!!!!! http://www.youtube.com/watch?v=7zp1TbLFPp8&feature=mfu_in_order&list=UL

  112. anonymous
    • 5 years ago
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    Dude u online???? i hope i didn't harm ur feelings!!!!!!!!

  113. anonymous
    • 5 years ago
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    no no i am still here. you can email at satellite73.openstudy@gmail.com

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