1. ## Quick differentiation help

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

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

is that correct so far? The book has the answer as $\displaystyle -4 x^3 (1-4 x^2)^2 (10 x^2-1)$, so I'm wondering if I was doing anything wrong.

2. This looks good so far.

3. Originally Posted by pickslides
This looks good so far.
$\displaystyle =-24x^5(1-4x^2)^2+4x^3(1-4x^2)^3$

This is where I get lost.

4. Originally Posted by youngb11
I'm trying to differentiate this function: $\displaystyle f(x)=x^4(1-4x^2)^3$

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

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

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