Calculus
posted by KIKSY .
Hi~ Thank you for your help!
I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way.
I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) at x = 0.
f(x) = 1/(x+2)
I tried to just write out the first and second and third derivatives, and this was fine, but then i got to the fourth and fifth derivatives and the quotient rule made the derivative look really confusing....is there a better way to approach this problem?
I might be doing this totally wrong since we just started learning Taylor series today in class, so any advice is much appreciated.

It turns out that if you had done your derivatives correctly, you would have found the rule:
for f(x)=1/(x+2)
f^{(n)}(x) = (1)^{(n)}n!/(x+2)^{n+1}
I got f^{(5)}(x)=120/(x+2)^{6}.
Hope that helps.