Chain rule. I'm trying to work some nth-order Taylor polynomial examples, but it seems like I've forgotten how to do the chain rule. If I have f(x)=cos(-6x) then I was thinking f'(x) would be [-sin(-6x)] times [-6], resulting in f'(x) = 6sin(-6x). However, my calculator and wolfram|alpha both say it is really [-6sin(6x)]. I believe them, but I'd really like to know what I forgot about dealing with the sign of the angle when applying the chain rule.

Question

Chain rule.  I'm trying to work some nth-order Taylor polynomial examples, but it seems like I've forgotten how to do the chain rule.  If I have f(x)=cos(-6x) then I was thinking f'(x) would be [-sin(-6x)] times [-6], resulting in f'(x) = 6sin(-6x).  However, my calculator and wolfram|alpha both say it is really [-6sin(6x)].  I believe them, but I'd really like to know what I forgot about dealing with the sign of the angle when applying the chain rule.

loser66 · Answer

yea, because sin (-x) = -sin x , hehehe

anonymous · Answer

oh.... I feel /really/ dumb right now.  But thank you!

loser66 · Answer

ok