Question

Anyone who have a formular to differentiate ln(x) 69 times? (I refuse to do it by hand)

Answer 1

ok, differentiate ln x . once
what u get ?

Answer 2

1/x -> -1/x^2 -> 2/x^3 and so on

Answer 3

so can't u generalize it in ters of n ?

Answer 4

*terms

Answer 5

So this perhaps?
f^(n)=(-1)^(n-1) (n-1)!x^(-n)

Answer 6

yup.

Answer 7

put n= 69

Answer 8

Hmmm that was surprisingly simple. but yes a exteamly long number becuase of the 68 factorial.

Answer 9

keep it as 68!

Answer 10

Sure thing, thanks. (just need to read about the gamma function then becuase i need to integrate soon)