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)? for part a) i got, please check for me. 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,... am i right so far, how do i do the other ones? Thanks.