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Math Help - Quick differentiation help

  1. #1
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    Quick differentiation help

    I'm trying to differentiate this function: f(x)=x^4(1-4x^2)^3

    =x^4(3)(1-4x^2)^2(-8x)+4x^3(1-4x^2)^3

    is that correct so far? The book has the answer as -4 x^3 (1-4 x^2)^2 (10 x^2-1), so I'm wondering if I was doing anything wrong.
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  2. #2
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    This looks good so far.
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  3. #3
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    Quote Originally Posted by pickslides View Post
    This looks good so far.
    =-24x^5(1-4x^2)^2+4x^3(1-4x^2)^3

    This is where I get lost.
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  4. #4
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    Quote Originally Posted by youngb11 View Post
    I'm trying to differentiate this function: f(x)=x^4(1-4x^2)^3

    =x^4(3)(1-4x^2)^2(-8x)+4x^3(1-4x^2)^3

    is that correct so far? The book has the answer as -4 x^3 (1-4 x^2)^2 (10 x^2-1), so I'm wondering if I was doing anything wrong.
    the book "answer" has been cleaned up algebraically. take your solution and factor out 4x^3(1-4x^2)^2 from each term ...

    4x^3(1-4x^2)^2[-6x^2 + (1-4x^2)] = 4x^3(1-4x^2)^2[1-10x^2] = -4x^3(1-4x^2)^2(10x^2-1)
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