find an explicit formula for the derivative of

so, i know

i'm not sure i see the pattern..(Wondering)

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- Apr 27th 2009, 03:29 PMbuttonbearnth derivative formula
find an explicit formula for the derivative of

so, i know

i'm not sure i see the pattern..(Wondering) - Apr 27th 2009, 03:44 PMderfleurer

I suggest looking now into that handy little ! operator. - Apr 27th 2009, 03:50 PMbuttonbear
sorry, i'm a little confused.. is there such a thing as (-n)! ? is that even what you're suggesting? you have to forgive me, i'm not very good at this :/

- Apr 27th 2009, 04:07 PMderfleurer
Google the Gamme function.

Easier way to get that negative, though:

When n is -4, we have a negative coefficient. -1^(n - 1)

*Edit*: Whoops. Technically, this isn't nth derivative. But you don't have to change much. =p

So, first derivative, we have -1x^-2, right? Formula says, first derivative means n = 1.

And n = 2?

Seems to work - Apr 27th 2009, 05:30 PMbuttonbear
okay, so.. i show work by just showing the calculation of the derivatives that you showed earlier?

thanks for your help! - Apr 27th 2009, 05:53 PMderfleurer
That should be good enough. But I don't know your instructor.

Show a few derivatives. Recognize patterns and relationships between numbers and the order of each derivative.

occurs @ 3rd-order derivative. So that's how you get

@ 3rd order derivative. So that's or

First order derivative has a negative coefficient, second has positive, third negative, fourth positive, etc. You know that every even gives a positive and every odd gives a negative. Hence

*Edit*: Another way to show the :

is the same as , right? So that's right there. - Apr 27th 2009, 09:56 PMbuttonbear
this was a very big help, thanks so much(Rofl)

- Apr 28th 2009, 03:04 AMHallsofIvy
Once you have "guessed" a formula for the nth derivative of 1/x, it should not be difficult to

**prove**it by induction on n.