Use Taylor series. In my calculations, the series for f(x) starts with , so the answer is 7.
>>>>>>> Question <<<<<<<<<
it is easy to find it generally but i was thinking that what if in some question ... say 100th differential is 0 ... there has to be a shortcut ... some help please
i even found out the general term of what differential would be after the third differential (when goes away)...
its
But i dont know how to find when will be non-zero
I have no idea what you are talking about. You can check in WolframAlpha that and for .
I don't know the answer because I don't know the exact class of problems you are referring to. For an arbitrary function f(x) given by its formula, I think the easiest way is to compute the nth derivative and evaluate it at 0. This particular problem seems to me to be designed to be solved using Taylor series. However, concerning problems that you may encounter during tests, etc., I don't know how similar to this one they will be.but isnt there is any general method to do these kind of problems