If f(x) = sin(x^3) find f^(15)(0)

  • Thread starter Calcotron
  • Start date
  • #1
17
0
Short and sweet, If f(x) = sin(x^3) find f^(15)(0) by which I mean find the 15th derivative of f. Do I have to write out all the derivatives and look for a pattern somewhere or is there an easier way?
 

Answers and Replies

  • #2
gel
533
5
Do you know the power series expansion for sin? If so, you can read off the derivatives from the Taylor series expansion
[tex]
f(x) = \sum_{n=0}^\infty\frac{x^n}{n!}f^{(n)}(0).
[/tex]
 
  • #3
17
0
Ok, so from the maclaurin series with x^3 substituted I get f(x) = x^3 - (x^9/ 3!) + (x^15/ 5!) and just from this I can see the 15th derivative of the function is going to be 15!/ 5!. Is that all correctÉ
 
  • #4
gel
533
5
yes!
 

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