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anonymous

  • one year ago

Take the derivative of: \[f(x)= \frac{ 5(2-x) }{ 3x^{1/3} }\]

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  1. Loser66
    • one year ago
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    Where are you stuck?

  2. Z4K4R1Y4
    • one year ago
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    use the quotient rule

  3. anonymous
    • one year ago
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    I tried using the quotient rule, I kept on getting the wrong answer. :(

  4. Loser66
    • one year ago
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    show work, please

  5. anonymous
    • one year ago
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    \[f'(x)=\frac{ -5(3x^{1/3}-10-5x(-x^{-4/3}) }{ 9x^{2/3} }\] I'm sure if this part is correct or not

  6. anonymous
    • one year ago
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    There is suppose to be a bracket between the exponent 1/3 and subtraction sign

  7. Loser66
    • one year ago
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    You MUST expand the parentheses before applying quotient rule OR let 5/3 in the front aside and take derivative the leftover by applying quotient rule. |dw:1433037281796:dw|

  8. Loser66
    • one year ago
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    Or |dw:1433037313347:dw|

  9. Loser66
    • one year ago
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    One more way: \(f(x) = \dfrac{10}{3}x^{-1/3} - \dfrac{5}{3}x^{2/3}\) , this form is the easiest one.

  10. Loser66
    • one year ago
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    got the last one?

  11. Loser66
    • one year ago
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    ok, \(\dfrac{1}{x} = x^{-1}\) right?

  12. anonymous
    • one year ago
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    Whooh! There's so many ways to this question.

  13. anonymous
    • one year ago
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    and yes, for 1/x

  14. Loser66
    • one year ago
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    \(f(x) = \dfrac{10-5x}{3x^{1/3}}\) ok?

  15. anonymous
    • one year ago
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    yes

  16. Loser66
    • one year ago
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    |dw:1433037860682:dw|

  17. Loser66
    • one year ago
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    |dw:1433037896740:dw|

  18. anonymous
    • one year ago
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    I got here: \[\frac{ -10 }{ 9 }^{-4/3}-\frac{ 10 }{ 9 }x^{-1/3}\]

  19. anonymous
    • one year ago
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    oops for I forgot the x. Is suppose to say x^(-4/3)

  20. Loser66
    • one year ago
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    yup, correct

  21. anonymous
    • one year ago
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    I'm not sure how to simplfy it more @Loser66

  22. Loser66
    • one year ago
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    just bring them down to the denominator |dw:1433038167229:dw|

  23. Loser66
    • one year ago
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    + in parentheses ( typo)

  24. Loser66
    • one year ago
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    To me, just let it as it is, you will have the full credit. No need to simplify.

  25. Loser66
    • one year ago
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    Because if you do more, it turns complicated since \(x^{4/3}=\sqrt[3] x^4\) ugly!!

  26. anonymous
    • one year ago
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    Just wondering if this is right? \[\frac{ 10(x+1) }{ 9^{4/3} }\]

  27. Loser66
    • one year ago
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    No

  28. Loser66
    • one year ago
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    I meant - infront.

  29. Loser66
    • one year ago
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    then you are right.

  30. anonymous
    • one year ago
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    oh oops! Thank you!

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