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Math Help - Help using the Power Rule

  1. #1
    Junior Member
    Joined
    Nov 2008
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    36

    Help using the Power Rule

    f(x)= 5x^5 (5x+6)^4

    I got 25*x^4 (5*x+6)^4 + 100*x^5 (5*x+6)^3

    But that's not right...

    Thanks
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  2. #2
    Member
    Joined
    Dec 2008
    From
    Auckland, New Zealand
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    189
    f(x) = 5x^5 (5x + 6)^4

    f '(x) = \frac{d}{dx} 5x^5 \times (5x + 6)^4 + \frac{d}{dx} (5x + 6)^4 \times 5x^5 \quad (chain rule)

    f '(x) = 25x^4 \times (5x + 6)^4 + 5 \times 4(5x + 6)^3 \times 5x^5 \quad

    f '(x) = 25x^4 (5x + 6)^4 + 100x^5(5x + 6)^3

    f '(x) = 25x^4 (5x + 6)^3 [(5x + 6) + 4x] \quad  (factorising)

    f '(x) = 25x^4 (5x + 6)^3 (9x + 6)

    f '(x) = 75x^4 (5x + 6)^3 (3x + 2)

    Is that the answer they're looking for?
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