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MTALHAHASSAN2

  • one year ago

can how we find the derivative of the following function 3sqrt x -1+x/x^4

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  1. anonymous
    • one year ago
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    ill help but you also have to try.

  2. MTALHAHASSAN2
    • one year ago
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    ok sure

  3. anonymous
    • one year ago
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    The answer is e3x√(32x−1/2) e3x(32x−1/2)

  4. anonymous
    • one year ago
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    Now I need a medal

  5. MTALHAHASSAN2
    • one year ago
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    @Redneckk__Lifee but how you get that

  6. anonymous
    • one year ago
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    online duhh. and why did you ask my name you already know it.

  7. anonymous
    • one year ago
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    I'm pretty sure I'm waiting for a medal!!!!!!

  8. marigirl
    • one year ago
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    Okay so we are differentiating \[\sqrt[3]{(x-1)}+ \frac{ x }{ x^4 }\] Is that the equation? I want to make sure its correct before we begin

  9. marigirl
    • one year ago
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    @MTALHAHASSAN2

  10. MTALHAHASSAN2
    • one year ago
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    @marigirl nope its wrong

  11. marigirl
    • one year ago
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    I meant- did i type your QUESTION correctly

  12. MTALHAHASSAN2
    • one year ago
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    |dw:1443775238584:dw|

  13. FireKat97
    • one year ago
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    so its \[f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }\] ???

  14. MTALHAHASSAN2
    • one year ago
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    nope

  15. FireKat97
    • one year ago
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    no, I mean is that the question?

  16. FireKat97
    • one year ago
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    @MTALHAHASSAN2

  17. MTALHAHASSAN2
    • one year ago
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    yes it is

  18. MTALHAHASSAN2
    • one year ago
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    ok wait a sec

  19. FireKat97
    • one year ago
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    okay, so what you want to start off doing, is bringing the \[x^4\] to the top, can you show me how you may do this?

  20. MTALHAHASSAN2
    • one year ago
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    @FireKat97 wait a sec

  21. FireKat97
    • one year ago
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    okay just tag me back whenever you're ready :)

  22. MTALHAHASSAN2
    • one year ago
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    |dw:1443777396971:dw|

  23. MTALHAHASSAN2
    • one year ago
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    here is the question

  24. MTALHAHASSAN2
    • one year ago
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    ok so we need to find the derivative of this

  25. FireKat97
    • one year ago
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    so its just like the one I'd typed up above?

  26. MTALHAHASSAN2
    • one year ago
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    oh yeah know i see

  27. FireKat97
    • one year ago
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    so firstly you want to start off by bringing the x^4 up to the top, can you do this and show me what you get?

  28. MTALHAHASSAN2
    • one year ago
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    sorry about that

  29. FireKat97
    • one year ago
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    nah, no problem :)

  30. MTALHAHASSAN2
    • one year ago
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    |dw:1443777684653:dw|

  31. anonymous
    • one year ago
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    haha

  32. MTALHAHASSAN2
    • one year ago
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    wait but why do we move 4

  33. FireKat97
    • one year ago
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    close, so I see you have brought up and distributed the x^4 and differentiated the 3x^1/2 and - x^-4, but you forgot about the - x^-3, do you see what i mean by this?

  34. FireKat97
    • one year ago
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    I find it easier to move it to the top, distribute it and then differentiate each of the terms

  35. FireKat97
    • one year ago
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    I'll show you what I mean

  36. MTALHAHASSAN2
    • one year ago
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    yeah plz i am confuse

  37. FireKat97
    • one year ago
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    \[f(x) = 3\sqrt{x} - \frac{ 1 + x }{ x^4 }\] = \[3\sqrt{x} - x ^{-4} (1 + x)\] do you see what I did here?

  38. MTALHAHASSAN2
    • one year ago
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    yeah know that's make a lot of scence

  39. FireKat97
    • one year ago
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    I simply brought the x^-4 into the numerator position and am now going to distribute it

  40. FireKat97
    • one year ago
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    yup so now we can distribute it like so \[3\sqrt{x} - x^{-4} - x^{-3}\] and now we can differentiate each of the terms, have a go

  41. FireKat97
    • one year ago
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    do you see how I got that?

  42. MTALHAHASSAN2
    • one year ago
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    wait how you get -x^3

  43. MTALHAHASSAN2
    • one year ago
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    oh i got u

  44. FireKat97
    • one year ago
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    okay so when we open up \[-x^{-4} (1 + x)\] we do \[-x^{-4} (1) -x^{-4} (x^1)\] and according to index laws, when we multiply something with the same base, we add th powers, so for e.g. \[(a^2).(a^3) = a^5\] so in the same way, \[(-x^{-4}).(x^1) = -x^{-4 + 1} = -x^{-3} \]

  45. FireKat97
    • one year ago
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    and now we have three separate terms, which we can differentiate

  46. FireKat97
    • one year ago
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    @MTALHAHASSAN2 did you try differentiating?

  47. MTALHAHASSAN2
    • one year ago
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    oh yeah i am trying it

  48. FireKat97
    • one year ago
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    oh okay :)

  49. MTALHAHASSAN2
    • one year ago
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    so are we left up with 3sqrt -x^-4 -x^-3

  50. FireKat97
    • one year ago
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    yup

  51. MTALHAHASSAN2
    • one year ago
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    and know we have to differentiating?

  52. MTALHAHASSAN2
    • one year ago
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    right

  53. FireKat97
    • one year ago
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    yeah we differentiate each of the terms

  54. MTALHAHASSAN2
    • one year ago
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    so for the sqrt is it be 1/2sqrt x

  55. FireKat97
    • one year ago
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    close

  56. MTALHAHASSAN2
    • one year ago
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    |dw:1443779376906:dw|

  57. FireKat97
    • one year ago
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    yup thats right!

  58. MTALHAHASSAN2
    • one year ago
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    and what about the x

  59. FireKat97
    • one year ago
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    the \[-x^{-4} - x^{-3}\]??

  60. MTALHAHASSAN2
    • one year ago
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    is it goona go in the denominater

  61. FireKat97
    • one year ago
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    we haven't differentiated those two terms yet..

  62. FireKat97
    • one year ago
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    not quite...

  63. FireKat97
    • one year ago
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    do you want me to show you?

  64. MTALHAHASSAN2
    • one year ago
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    yes plz

  65. FireKat97
    • one year ago
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    okay so you know how we have \[f(x) = 3x^{1/2} -x^{-4} -x^{-3}\] you did well in correctly being able to differentiate the first term, but we still have two terms left to differentiate so we should get \[f'(x) = \frac{ 3 }{ 2\sqrt{x} } -(-4)x^{-4-1} -(-3)x^{-3-1} \] which can further simplify down to \[f'(x) = \frac{ 3 }{ 2\sqrt{x} } + 4x^{-5} + 3x^{-4}\] does that make sense?

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