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Math Help - Derivatives

  1. #1
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    Derivatives

    I'm stuck with these derivative problems. I've tried all the methods that I know and haven't gotten anything.

    1. Find f'(x) where f(x) = sqrt(4x). Then find f'(5)

    2. Find f'(x) where f(x) = 4x^2 - 3x - 27

    3. Find f'(x) where f(x) = 4 + 2/x + 6/x^2

    4. Find f'(9) where f(x) = 3(sqrt(x))(x^3 - 8(sqrt(x)) + 5)

    5. Find f'(x) where f(x) = 12/(t^5)
    Last edited by john11235; October 12th 2008 at 11:29 AM.
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  2. #2
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    Quote Originally Posted by john11235 View Post
    I'm stuck with these derivative problems. I've tried all the methods that I know and haven't gotten anything.

    1. Find f'(x) where f(x) = sqrt(4x). Then find f'(5)

    Mr F says: {\color{red}f(x) = 2 \sqrt x = 2 x^{1/2}}.

    2. Find f'(x) where f(x) = 4x^2 - 3x - 27

    3. Find f'(x) where f(x) = 4 + 2/x + 6/x^2

    Mr F says: {\color{red}f(x) = 4 + 2 x^{-1} + 6 x^{-2}}.

    4. Find f'(9) where f(x) = 3(sqrt(x))(x^3 - 8(sqrt(x)) + 5)

    Mr F says: Expand.

    5. Find f'(x) where f(x) = 12/(t^5)

    Mr F says: {\color{red}f(t) = 12 t^{-5}}.
    In all cases, use the first rule you would have been taught: If f(x) = a x^n then f'(x) = n a x^{n-1}.

    Differentiate term-by-term as required. Then substitute the given value of x.
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