derivative

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29) Find the derivative of the function.

F(X)=2x^2(3-4x)^2

This is what I have so far. I am usually pretty good at simplifying but I am missing something here.

f'(x)=2x^2(4)(3-4x)^3(-4) + (3-4x)^4(4x)

Here is where I go wrong. (Answer from book)
=4x(3-4x)^3(-12+3)

Thanks for your help.

  • derivative -

    Should be =4x(3-4x)^3(-12x+3)

  • derivative -

    F(X)=2x^2(3-4x)^2

    This is what I have so far. I am usually pretty good at simplifying but I am missing something here.

    f'(x)=2x^2(4)(3-4x)^3(-4) + (3-4x)^4(4x)

    Here is where I go wrong. (Answer from book)
    =4x(3-4x)^3(-12+3)
    =================================
    I get
    F(X)=2x^2(3-4x)^2
    f' = 2x^2 (2)(3-4x)(-4) +(3-4x)^2(4x)
    = -16x^2(3-4x)+4x(3-4x)^2
    = 4x(3-4x)(3-4x) -16x^2(3-4x)
    = 4x(3-4x)(3-4x) -4x(3-4x)(4x)
    = 4x(3-4x)(3-4x-4x)
    =4x(3-4x)(3-8x)

  • derivative -

    F(X)=2x^2(3-4x)^2
    another way
    f(x) = 2x^2(9 - 24x +16 x^2)
    = 18 x^2 - 48 x^3 +32 x^4
    take the derivative of that
    = 36 x - 144 x^2 + 128 x^3
    = 4x ( 9 - 36 x + 32 x^2)
    = 4 x (3-4x)(3-8x)

    Unless you have a typo, I have it right and the book has it wrong.

  • derivative -

    The final answer in the book is

    (-12x)(4x-1)(3-4x)^3

    This book has had several errors so far.

  • derivative -

    In google type:
    wolfram alpha

    When you see list of results click on:
    Wolfram Alpha:Comutation Knowledge Engine

    When page be open in rectangle type:
    2x^2(3-4x)^2
    and click option =

    After few seconds you will see everything about that function.

    Then click option

    Derivative: Show steps

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