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moongazer

  • 2 years ago

find the derivative: Y(x) = 1/sqrt x please check my answer :)

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  1. moongazer
    • 2 years ago
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    |dw:1347972647599:dw|

  2. moongazer
    • 2 years ago
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    I used the definition

  3. m_charron2
    • 2 years ago
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    Yes, that seems essentially correct. However, I've never seen it written this way. Usually, we group up the Xs, so you'd get this : |dw:1347971974141:dw|

  4. m_charron2
    • 2 years ago
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    or this : |dw:1347971995093:dw|

  5. moongazer
    • 2 years ago
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    What is the correct (best) way to right the derivative of a function? isn't it that there should be no radical in the denominator ? that's why I made it that way :)

  6. mathslover
    • 2 years ago
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    \[\large{\frac{d}{dx}\frac{1}{\sqrt{x}}}\] \[\large{\frac{d}{dx}{\sqrt{x}^{-1}}}\] \[\large{\frac{d}{dx}x^{-\frac{1}{2}}}\] \[\large{\frac{-1}{2\sqrt{x^3}}}\]

  7. mathslover
    • 2 years ago
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    this is what I did. .. well do you mean by rationalizing? @moongazer

  8. moongazer
    • 2 years ago
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    yes, do you still need to rationalize it ?

  9. mathslover
    • 2 years ago
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    If u will then it will look ugly.. let it be in this way

  10. ParthKohli
    • 2 years ago
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    Yeah, you may rationalize if you need.

  11. ParthKohli
    • 2 years ago
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    Rationalizing beautifies the fraction; it doesn't make it ugly. lol

  12. mathslover
    • 2 years ago
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    or u can right : \[\large{\frac{-1}{2x^{\frac{3}{2}}}}\]

  13. mathslover
    • 2 years ago
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    lol \[\large{\frac{-1\times x^{\frac{3}{2}}}{2x^3}}\]

  14. mathslover
    • 2 years ago
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    \[\large{\frac{-\sqrt{x^3}}{2x^3}}\] @moongazer

  15. mathslover
    • 2 years ago
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    got it @moongazer ?

  16. moongazer
    • 2 years ago
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    yes, based on your answers, Does it mean that you can write the derivative of a function in anyway you like as long as it doesn't change the meaning of your derivative? it could be in exponential,rationalized, not rationalized or any other forms.

  17. moongazer
    • 2 years ago
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    @mathslover

  18. mathslover
    • 2 years ago
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    yes

  19. moongazer
    • 2 years ago
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    Thanks :)

  20. m_charron2
    • 2 years ago
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    Also, if you choose to keep it simply as \[\frac{ -1 }{ 2x^{3/2} }\] is that it makes it simpler if you need to find its derivative after that (because sometimes, they just love to have you chain-derive something)

  21. moongazer
    • 2 years ago
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    Thanks for the info :)

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