# Quick differentiation help

• Feb 17th 2011, 02:55 PM
youngb11
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.
• Feb 17th 2011, 03:02 PM
pickslides
This looks good so far.
• Feb 17th 2011, 03:03 PM
youngb11
Quote:

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.
• Feb 17th 2011, 03:04 PM
skeeter
Quote:

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)\$