calculus
posted by eric on .
i need to find the derivative using chain rule:
(x^2 + 2x  6)^2 (1x^3)^2
i got the answer from a site but the problem is i cannot get my work to match up with the answer, i don't know what im doing wrong.
answer: 10x^9 + 36x^8 − 64x^7 − 182x^6 + 168x^5 + 80x^4 + 196x^3 − 204x^2 − 16x−24
my work:
f'(x) = [2(x^2 + 2x  6)*(2x + 2)]*(1x^3)^2 + [2(1x^3)*(3x^2)]*(x^2 +2x6)^2
f'(x)=2(2x^3 +6x^2 8x12)*(1x^3)^2 +[2(3x^2 3x^5)]*(x^2 +2x6)(x^2 +2x6)
f'(x)= (4x^3 +12x^2 16x24)*(12x^3 +x^6) +(6x^2 6x^5)*(x^4 +4x^3 8x^2 24x+36)
f'(x)=4x^9 +12x^8 16x^7 32x^6 24x^5 +32x^4 +52x^3 +12x^2 16x24)+(6x^9 24x^8 +48x^7 138x^6 198x^5 48x^4 144x^3 +216x^2)
f'(x)=2x^9 12x^8 +32x^7 170x^6 +222x^5 16x^4 92x^3 +228x^2 16x 24
its 1am and i could have made some arithmetic errors but im fairly certain there accurate for the most part

well, maybe they're as accurate as your spelling...
Your very first line is in error: should be 3x^2 toward the end.
Fix that, and everything's ok.
If you visit wolframalpha.com and enter
derivative (x^2 + 2x  6)^2 (1x^3)^2
you will get several different ways of writing it.
If you enter
your corrected first step:
[2(x^2 + 2x  6)*(2x + 2)]*(1x^3)^2 + [2(1x^3)*(3x^2)]*(x^2 +2x6)^2
you will get the same answer.
Devil's in the details, as usual. Unless otherwise instructed, I'd probably not take it all the way to a single expanded expression. 
Y=2x^316x^2+64x+1