Find the derivative

[stephier]

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

this is what i have so far...
f'(x)=2x^2(4)(3-4x)^3(-4)+(3-4x)^4(4x)

according to the solutions manual the next step is.....
=4x(3.4x)^3(-8x+3-4x)

I am not getting the same answer. Can someone break it down for a calculus newb?

 

[tkhunny]

Why are you looking at the solutions before you are done? Try finding common factors in the two terms you have created.

 

[mmm4444bot]

this is what i have so far...

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

This is the correct first derivative for f(x).

You're trying to simplify that expression?

I'll start a simplification by using the Commutative Property of Multiplication to rearrange some factors:

(2)(4)(-4)(x^2)(3 - 4x)^3 + (4)(x)(3 - 4x)^4

I am not getting the same answer [as the book].

The expression for f`(x) can be written in different forms.

As I noted, your posted result is already correct.

After simplifying it, you could also factor, as suggested by tkhunny.

You could also multiply everything (i.e., "expand it"), if you want to practice FOILing.

f`(x) = 324x - 2592x^2 + 6912x^3 - 7680x^4 + 3072x^5

Did they request the answer in some specific form?

If not, I would simplify your result by doing the easy arithmetic and leave it at that.