Taylor Series for cos(x^5) | Computing f^(90)(0) | Homework Solution

[eifphysics]

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 Tyler Series form and solve for f^(90)(0), but it gave me a wrong answer.

 

[Mark44]

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.

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

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

 

[eifphysics]

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

 

[Mark44]

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

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).