Math Is Fun Forum

darkdr

Member

Registered: 2009-04-21

Posts: 2

n-th derivative term from a function

hi i'd like to know how to calculate by Taylor's series the n-th derivative term from a function.. Example i've the

and i for example the term 2006 with x=0:

help me

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: n-th derivative term from a function

you should be able to get an expression for the nth derivitive:

the bottom of the fraction is simple, the top follows the pattern:

1 -> 2 x 1
2 -> 2x2 x 1
3 -> 2x2x2 x 1x2
4 -> 2x2x2x2 x 1x2x3
5 -> 2x2x2x2x2 x 1x2x3x4
6 -> 2x2x2x2x2x2 x 1x2x3x4x5

n -> 2^n(n-1)!

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if you are instead allowed to use the mclaurin series for ln(1-x) then you have:

then:

which gives you:

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in either case (using windows calculator)

Last edited by luca-deltodesco (2009-04-21 23:32:18)

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darkdr

Member

Registered: 2009-04-21

Posts: 2

Re: n-th derivative term from a function

thanks man, that's it xD