# derivative

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)

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

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2. 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)

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3. 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.

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4. The final answer in the book is

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

This book has had several errors so far.

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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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