Hello...

BIG question (big for me, at least): Is there a general formula for the n-th derivative of

Basically I have a function exactly like that and I need to extract the n-th derivative.

THANKS in advance

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- Jan 31st 2008, 10:41 AMpaolopiacen-th derivative of u'exp(u)
Hello...

BIG question (big for me, at least): Is there a general formula for the n-th derivative of

Basically I have a function exactly like that and I need to extract the n-th derivative.

THANKS in advance - Jan 31st 2008, 11:07 AMcolby2152
- Jan 31st 2008, 09:27 PMmr fantastic
There's a formula for taking the nth derivative of any function of the form y = f(x) g(x) called Leibniz's Rule.

- Jan 31st 2008, 10:35 PMpaolopiaceThanks. I know the Leibniz rule. I just wanted...
...to see if there is a more simple and straightforward rule for u'exp(u).

- Jan 31st 2008, 10:42 PMcurvature
- Feb 1st 2008, 05:04 AMcolby2152
- Feb 1st 2008, 06:17 AMOpalg
If then , where is some polynomial in u and its derivatives. If you differentiate one more time then you get . So . If you apply this recursive formula to find the first few derivatives then you get

,

,

,

.

That should be enough to convince you that there is not going to be any simple formula for the n-th derivative. :(