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mathcalculus

  • one year ago

Derivative Question: Help (attached below)

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  1. mathcalculus
    • one year ago
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  2. NoelGreco
    • one year ago
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    Get rid of the radicals.

  3. satellite73
    • one year ago
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    hint:\[ x^5\sqrt{x}=x^{5+\frac{1}{2}}=x^{\frac{11}{2}}\]

  4. mathcalculus
    • one year ago
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    right.. 3x^(11/2)

  5. NoelGreco
    • one year ago
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    That's it, and go with a negative exponent on the second term to avoid the quotient rule.

  6. mathcalculus
    • one year ago
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    + -4*x^-7/2 ?

  7. NoelGreco
    • one year ago
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    Yes.

  8. mathcalculus
    • one year ago
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    i got: 3x^(11/2)+14/x^9/2..

  9. mathcalculus
    • one year ago
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    @NoelGreco

  10. NoelGreco
    • one year ago
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    \[3x ^{\frac{ 11 }{ 2 }}-4x ^{\frac{ -7 }{ 2 }}\] Now take the derivative.

  11. mathcalculus
    • one year ago
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    14x/x^9/2

  12. mathcalculus
    • one year ago
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    ?

  13. NoelGreco
    • one year ago
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    The derivative of the second term is\[\frac{ d }{ dx }3x ^{\frac{ 11 }{ 2 }}=\frac{ 33 }{ 2 }x ^{\frac{ 9 }{ 2 }}\] I don't know how you're trying to take the derivative, but you simply use the power rule on each term.

  14. mathcalculus
    • one year ago
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    huh?

  15. mathcalculus
    • one year ago
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    from 3x^ (11/2) + 14x^(-9/2)

  16. mathcalculus
    • one year ago
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    doesn't the x9/2 down

  17. mathcalculus
    • one year ago
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    @NoelGreco hey sorry to interrupt. but i just needed to figure this out before leaving..

  18. satellite73
    • one year ago
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    \[\frac{d}{dx}14x^{-\frac{9}{2}}=-\frac{9}{2}\times 14x^{-\frac{9}{2}-1}\]whatever that is

  19. mathcalculus
    • one year ago
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    this is my work so far:

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  20. sami-21
    • one year ago
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    Before applying the power rule combine the terms as told you previously . \[\Large f(x)=3x^5.x^\frac{1}{2}-\frac{-4}{x^3.x^\frac{1}{2}}\] combining the terms \[\Large f(x)=3x^\frac{11}{2}-\frac{4}{x^\frac{7}{2}}\] \[\Large f(x)=3x^\frac{11}{2}-4x^{-\frac{7}{2}}\] now Apply the Power rule.

  21. mathcalculus
    • one year ago
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    thank you are you still there @sami-21

  22. mathcalculus
    • one year ago
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    i have one question if you dont mind

  23. mathcalculus
    • one year ago
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    what if they ask: derivative of sqrt(6x)

  24. mathcalculus
    • one year ago
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    i dont know why i always messed them up

  25. mathcalculus
    • one year ago
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    i thought it would be like this: = 6x^(1/2) then =3x^(-1/2) =3/(x^(1/2)

  26. mathcalculus
    • one year ago
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    @sami-21

  27. sami-21
    • one year ago
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    yes that is correct.

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