The discussion revolves around finding the 90th derivative of the function f(x) = cos(x^5) at x = 0 using its Taylor series expansion. Participants are exploring the implications of substituting x^5 into the Taylor series for cos(x).
Some participants are attempting to clarify the substitution process and its impact on the series coefficients. Guidance has been offered regarding the correct series form and the importance of expressing the series in an expanded format.
There is a noted confusion regarding the notation for superscripts and subscripts, which may affect participants' ability to communicate their mathematical expressions clearly.
Show us what you got when you did the substitution. That's the right approach.Minjie said:Homework Statement
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?
Homework Equations
The Attempt at a Solution
I tried to substitute x^5 into x's Taylor Series form and solve for f^(90)(0), but it gave me a wrong answer.
Nothing changes in that part. In your formula above, replace x by x5. That will be your Taylor series for cos(x5).Minjie said: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.