need help diiferentiating the second part of taylor series

[calcnoob145]

this is the problem i have dealing with the taylor series


so the problem is the second differentation f"(x) where am i going wrong with my differentation

and i alway end up with 1/1458 and not 1/5832 which is the correct answer

 

[lookagain]

this is the problem i have dealing with the taylor series
View attachment 2772View attachment 2773View attachment 2774

so the problem is the second differentation f"(x) where am i going wrong with my differentation

and i alway end up with 1/1458 and not 1/5832 which is the correct answer

Your arithmetic is off:

\(\displaystyle \dfrac{\bigg(\dfrac{-1}{2916}\bigg)}{2!} \ \ne \ \dfrac{-1}{1458}\)


Instead, \(\displaystyle \ \ \dfrac{\bigg(\dfrac{-1}{2916}\bigg)}{2!} \ = \ \dfrac{-1}{2916} \ \div \ 2 \ = \ \dfrac{-1}{2916}\bigg(\dfrac{1}{2}\bigg) \ = \ \dfrac{-1}{5832}\)

 

[calcnoob145]

oo wow its something simple that threw me off thanks got it