Homework Help: Taylor Series Problem

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1. Jan 11, 2015

eifphysics

1. The problem statement, all variables and given/known data

Let f(x)=cos(x^5). By considering the Taylor series for f around 0, compute f^(90)(0).
by the way, I don't know how super/sub script works?
2. Relevant equations

3. The attempt at a solution
I tried to substitute x^5 into x's Tyler Series form and solve for f^(90)(0), but it gave me a wrong answer.

2. Jan 11, 2015

Staff: Mentor

Show us what you got when you did the substitution. That's the right approach.

BTW, it's Taylor series, not Tyler series.

3. Jan 12, 2015

eifphysics

cosx=∑(-1)^n/(2n)!*x^2n
I am not sure what the an part: (-1)^n/(2n)! will becomes when I substitute x5 into the series.

4. Jan 12, 2015

Staff: Mentor

Nothing changes in that part. In your formula above, replace x by x5. That will be your Taylor series for cos(x5).

It might be helpful to write the new series in expanded form rather than in closed form (as a summation).