Maclaurin Polynomial

  • Thread starter me9900
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  • #1
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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.
 

Answers and Replies

  • #2
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Hint: Maclaurin polynomial may be helpful to you.
Do you know the Maclaurin series for sin(x)?
 
  • #3
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yes but how does the x^2 alter the expansion?
 
  • #4
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Replace each occurrence of x in the Maclaurin series expansion for sin(x) with x^2.
 
  • #5
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So the expansion would be:

x^2-x^6/3!+x^10/5! ?
 
  • #6
35,439
7,308
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.
 
  • #7
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Thanks
 

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