f(x) =ln (1-x)

a) Compute f'(x), f''(x), f'''(x). Spot the pattern and give an expression for f ^(n) (x) [the n-th derivative of f(x)]

b) Compute the MacLaurin series of f(x) (i.e. the Taylor series of f(x) around x=0)

c) Compute the radius of convergence and determine the interval of convergence of the series in b).

d) Determine the Taylor series of f'(x) around x=0. Can you do so without using b)?

e) How would you have computed part b) if you had first done part d)?

I did part a) (hope its right)

f'(x) = -1/(1-x)

f''(x) = -1/(1-x)^2

f'''(x) = -2/(1-x)^3

f^(n) (x) = -((n-1)!)/(1-x)^n

for n = 1,2,3,...

I am not too sure for the other ones, thanks for any help.