sophiagrace
New member
- Joined
- Sep 8, 2021
- Messages
- 3
Good for you for correcting the notation above to [imath]D_x\left[\displaystyle{x^2}\int_0^x {\cos \left( {{t^3}} \right)dt}\right] [/imath]Let View attachment 28827
Compute the derivatives View attachment 28828
I began constructing the series for x^2 cos x^3, but I am having trouble finding a shortcut to take 15 derivatives so I don't have to do them all out.
Hopefully somebody can help me. Thanks!
Yes, I think I was confusing the two. The 15th derivative would be the 16th term, correct? If that's the case, I'm still getting the same term I have shown at the bottom of my work...I think you're confusing the 15th derivative with the 15th term!
What term of a Maclaurin series contains the 15th derivative of the function? Write out what that term is.
Then compare that term to one you have already written! (Well, you haven't actually written it yet, because you didn't distribute.)
Do you really think that the series for cos x ends, that is it is not an infinite series???View attachment 28835
Here is what I have so far. I built the series for Cos (x^3) and then integrated that series. I tried to find the pattern and apply it to find the 15th derivative, but it seems like I skipped a step...
No, it's the term containing x^15! It's the 16th term only if you show all terms, including those that are zero!Yes, I think I was confusing the two. The 15th derivative would be the 16th term, correct? If that's the case, I'm still getting the same term I have shown at the bottom of my work...