Question

find
nth
derivative of log(1-x)​

Answer 1

Answer:

Using yn as the nth derivative,

y = ln(1+x)

y1 := 1/(1+x)

y2 := -1/(1+x)^2

y3 := 2/(1+x)^3

y4 := -6/(1+x)^4

y5 := 24/(1+x)^5

By observation, we can see that the nth derivative will be given by

yn = (-1)^(n-1).(n-1)! / (1+x)^n, n >= 1