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Alright, here is the derivatives problem. I couldn't make it easy, I hope you realize, hon. :P

Consider the function given by:

Show that

for any n greater than or equal to zero.

(And f with a superscript mark represents the number of derivatives from f(x).)

"If I die of a heart attack eating bacon, I'll be a happy man." -My father

This post was edited by Hawkeye on Mar 27, 2006.

Http://www.sosmath.com/calculus/diff/derpro01/answer6.html

Since nobody wants to take a crack at it, you've defenestrated your chances of trying. Here you are. :P

Challenging but not impossible.

It is really only a matter of getting a formula in terms of f''(x), f'(x) and f(x), and proving that, then show by induction that if fn+2(x), fn+1(x), and fn(x) is true, then fn+3(x), fn+2(x), fn+1(x) is also true.

"If I die of a heart attack eating bacon, I'll be a happy man." -My father