I think you can see a pattern here...
Find an expression for the nth derivative of f(x)=e^(x) * sin(x)
so what would the nth derivative of f be: f^(n) (x)
You can make a different expression for odd or even numbers, but I still can't quiet get one that works.
Please show me one that would work!!!
You could use the sum notation. For the nth derivative, you start with (n-1)th derivative + , and then do the sum of all the lower order derivatives and the original function.. don't forget the minus sign... It should look something like this:
This gives the expression for all the th derivatives of the function (so ), assuming the sum term is ignored if .
That being said, I don't really see the point in doing this. It's not like that new expression is easier to use or something. Do you have any other information associated with this, perhaps the context would make it easier to know what you are really asking for (because I'm not sure this is what you want).