derivative
posted by Steff on .
29) Find the derivative of the function.
F(X)=2x^2(34x)^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)(34x)^3(4) + (34x)^4(4x)
Here is where I go wrong. (Answer from book)
=4x(34x)^3(12+3)
Thanks for your help.

Should be =4x(34x)^3(12x+3)

F(X)=2x^2(34x)^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)(34x)^3(4) + (34x)^4(4x)
Here is where I go wrong. (Answer from book)
=4x(34x)^3(12+3)
=================================
I get
F(X)=2x^2(34x)^2
f' = 2x^2 (2)(34x)(4) +(34x)^2(4x)
= 16x^2(34x)+4x(34x)^2
= 4x(34x)(34x) 16x^2(34x)
= 4x(34x)(34x) 4x(34x)(4x)
= 4x(34x)(34x4x)
=4x(34x)(38x) 
F(X)=2x^2(34x)^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 (34x)(38x)
Unless you have a typo, I have it right and the book has it wrong. 
The final answer in the book is
(12x)(4x1)(34x)^3
This book has had several errors so far. 
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(34x)^2
and click option =
After few seconds you will see everything about that function.
Then click option
Derivative: Show steps