T thebenji New member Joined Sep 2, 2006 Messages 31 Dec 6, 2006 #1 How do i use mclaurin series to find high-numbered derivatives of functions? for example: the 10th derivative of arctan(x^2/6) at x=0 or the 9th derivative of [cos(4x^2)-1]/x^3 at x=0 ?
How do i use mclaurin series to find high-numbered derivatives of functions? for example: the 10th derivative of arctan(x^2/6) at x=0 or the 9th derivative of [cos(4x^2)-1]/x^3 at x=0 ?
tkhunny Moderator Staff member Joined Apr 12, 2005 Messages 11,325 Dec 6, 2006 #2 The first derivative might give more clues than the original function. \(\displaystyle \frac{d}{dx}atan(\frac{x^{2}}{6})\;=\;\frac{12x}{x^{4}+36}\) What does that series look like? Perhaps you discussed a specific idea in class?
The first derivative might give more clues than the original function. \(\displaystyle \frac{d}{dx}atan(\frac{x^{2}}{6})\;=\;\frac{12x}{x^{4}+36}\) What does that series look like? Perhaps you discussed a specific idea in class?
T thebenji New member Joined Sep 2, 2006 Messages 31 Dec 6, 2006 #3 I don't see anything. I know that arctan(x) = summation(1-)^n*[x^(2n+1)]/(2n+1). Am I supposed to use that somehow?
I don't see anything. I know that arctan(x) = summation(1-)^n*[x^(2n+1)]/(2n+1). Am I supposed to use that somehow?
