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Math Help - Differentiate simple question.

  1. #1
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    Differentiate simple question.

    Differentiate:



    I know that r^6 changes to 6r^5, r changes to 1, and the -1 is eliminated because it turns to 0.. but i'm kind of confused what to do with the - 2/5squareroot of r

    Do I have to use the quotient rule? Or is it just bringing 5(r)^1/2 to the numerator, changing it to r^-1/2 and multiplying it by -2.

    So (-2)(5)(r)^-1/2
    =-10r^-1/2
    power rule:
    5r^-3/2?
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  2. #2
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    You seem to be close. How did the '5' get into the numerator?
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    MHF Contributor harish21's Avatar
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    Quote Originally Posted by kmjt View Post
    Differentiate:



    I know that r^6 changes to 6r^5, r changes to 1, and the -1 is eliminated because it turns to 0.. but i'm kind of confused what to do with the - 2/5squareroot of r

    Do I have to use the quotient rule? Or is it just bringing 5(r)^1/2 to the numerator, changing it to r^-1/2 and multiplying it by -2.

    So (-2)(5)(r)^-1/2
    =-10r^-1/2
    power rule:
    5r^-3/2?
    let the 2/5 part be as it is. Just find the derivative of 1/sqrt(r)

    which will be (-1/2)*r^-3/2

    So your answer should be

    6r^5 + 1/(5r^(3/2))+1
    Last edited by harish21; March 9th 2010 at 07:57 PM. Reason: incorrectly done before
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    Hoow would I write that not as a fraction?
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  5. #5
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by kmjt View Post
    Hoow would I write that not as a fraction?
    6r^5 + (1/5)*r^-(3/2)+1

    Is this what you mean by writing it NOT as a fraction?
    Last edited by harish21; March 9th 2010 at 08:35 PM.
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    Quote Originally Posted by harish21 View Post
    6r^5 + 5*r^-(3/2)+1

    Is this what you mean by writing it NOT as a fraction?
    5r^-3/2.. so I did do it right in my initial attempt?
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  7. #7
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by kmjt View Post
    Differentiate:



    I know that r^6 changes to 6r^5, r changes to 1, and the -1 is eliminated because it turns to 0.. but i'm kind of confused what to do with the - 2/5squareroot of r

    Do I have to use the quotient rule? Or is it just bringing 5(r)^1/2 to the numerator, changing it to r^-1/2 and multiplying it by -2.

    So (-2)(5)(r)^-1/2
    =-10r^-1/2
    power rule:
    5r^-3/2?
    the derivative of this part is calculated this way:

    -2 /5*-1/2 *r^(-3/2)


    Thats where the 2s get cancelled and you are left with

    (1/5)*r^(-3/2)
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  8. #8
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by kmjt View Post
    5r^-3/2.. so I did do it right in my initial attempt?
    I am sorry.. its not 5r^-3/2

    Its (1/5) r^-3/2
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