# Homework Help: Maclaurin Polynomial

1. Dec 15, 2008

### me9900

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

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

2. Relevant equations
The taylor expansion/maclaurin expansion for sin.

3. The attempt at a solution
Help.

2. Dec 15, 2008

### Staff: Mentor

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

3. Dec 15, 2008

### me9900

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

4. Dec 15, 2008

### Staff: Mentor

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

5. Dec 15, 2008

### me9900

So the expansion would be:

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

6. Dec 15, 2008

### Staff: Mentor

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.

7. Dec 15, 2008

Thanks