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Math Help - Differentiation problem

  1. #1
    Ant
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    Differentiation problem

    Hi,

    I'm mistified about where I'm going wrong here:

    Find the derivative of: [(4x-1)(4x-1)^1/2]

    The answer given is 6(4x-1)^1/2

    but I get 6(4x -1)

    not sure where i'm going wrong if anyone could help that would be great!

    Thanks.
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  2. #2
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    Quote Originally Posted by Ant View Post
    Hi,

    I'm mistified about where I'm going wrong here:

    Find the derivative of: [(4x-1)(4x-1)^1/2]

    The answer given is 6(4x-1)^1/2

    but I get 6(4x -1)

    not sure where i'm going wrong if anyone could help that would be great!

    Thanks.
    y = (4x-1)(4x-1)^{\frac{1}{2}} = (4x-1)^{\frac{3}{2}}

     <br />
y' = \frac{3}{2}(4x-1)^{\frac{1}{2}} \cdot 4<br />

    y' = 6(4x-1)^{\frac{1}{2}}
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  3. #3
    Ant
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    Thanks, that makes perfect sense.

    could you explain what's wrong with my method please?

    u = 4x-1
    u' = 4
    v = (4x-1)^1/2
    v' = 2/[(4x-1)^1/2]

    using product rule --

    4(4X-1)1/2 + 2(4x-1)/[(4x-1)^1/2]

    multiplying through by (4x-1)^1/2

    4(4x-1) + 2(4x-1) = 24x-6 = 6(4x-1)

    I know i'm going wrong somewhere..I just can't see where!
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  4. #4
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    Quote Originally Posted by Ant View Post
    Thanks, that makes perfect sense.

    could you explain what's wrong with my method please?

    u = 4x-1
    u' = 4
    v = (4x-1)^1/2
    v' = 2/[(4x-1)^1/2]

    using product rule --

    4(4X-1)1/2 + 2(4x-1)/[(4x-1)^1/2]

    multiplying through by (4x-1)^1/2

    no, you have to multiply through by 1 ...
    \textcolor{red}{\frac{(4x-1)^{\frac{1}{2}}}{(4x-1)^{\frac{1}{2}}}}

    4(4x-1) + 2(4x-1) = 24x-6 = 6(4x-1)

    I know i'm going wrong somewhere..I just can't see where!
    .
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  5. #5
    Ant
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    thanks, of course!

    I thiink I was trying to treat the plus sign like it was an equals sign...
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