please show me how to solve the following.http://f20.yahoofs.com/hkblog/_9eQUJ..._____DH_9lrq2O

i have tried differentiation twice , but i cant get the same results..

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- Sep 23rd 2009, 08:38 AMkinHigher order derivatives
**please show me how to solve the following.**http://f20.yahoofs.com/hkblog/_9eQUJ..._____DH_9lrq2O

i have tried differentiation twice , but i cant get the same results..

- Sep 23rd 2009, 03:06 PMJester
First, I believe there's a typo. I think it should be and not .

If you consider

then differentiating both sides wrt twice and adding the same expression gives

Expanding gives - the first result.

If we let then we have the hierarchy of differential equations

.

By induction we can show that

and at

Substitution into (1) leads to the second result

. - Sep 23rd 2009, 07:48 PMkin