Posted by eric on Monday, January 13, 2014 at 3:00am.
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

calculus  Steve, Monday, January 13, 2014 at 5:10am
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. 
calculus  mary, Monday, March 2, 2015 at 7:38pm
Y=2x^316x^2+64x+1