# Maclaurin Polynomial

## Homework Statement

Compute the sixth derivative of f(x)=sin(x^2) at x=0. Hint: Maclaurin polynomial may be helpful to you.

## Homework Equations

The taylor expansion/maclaurin expansion for sin.

## The Attempt at a Solution

Help.

Mark44
Mentor
Hint: Maclaurin polynomial may be helpful to you.
Do you know the Maclaurin series for sin(x)?

yes but how does the x^2 alter the expansion?

Mark44
Mentor
Replace each occurrence of x in the Maclaurin series expansion for sin(x) with x^2.

So the expansion would be:

x^2-x^6/3!+x^10/5! ?

Mark44
Mentor
So the expansion would be:

x^2-x^6/3!+x^10/5! ?

That would be the first three nonzero terms, yes. Keep in mind there are quite a few terms whose coefficients are zero, so sin(x^2) = 0 + 0x + x^2 + 0x^3 + 0x^4 + 0x^5 - x^6/3! + ...

Regarding your original problem, keep in mind the general formula for the Maclaurin series, and how you get the coefficients of the various powers of x.

Thanks