posted by eric .
i need to find the derivative using chain rule:
(x^2 + 2x - 6)^2 (1-x^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
f'(x) = [2(x^2 + 2x - 6)*(2x + 2)]*(1-x^3)^2 + [2(1-x^3)*(3x^2)]*(x^2 +2x-6)^2
f'(x)=2(2x^3 +6x^2 -8x-12)*(1-x^3)^2 +[2(3x^2 -3x^5)]*(x^2 +2x-6)(x^2 +2x-6)
f'(x)= (4x^3 +12x^2 -16x-24)*(1-2x^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 -16x-24)+(-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 (1-x^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)]*(1-x^3)^2 + [2(1-x^3)*(-3x^2)]*(x^2 +2x-6)^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.