let-give-f-x-x-4x-2-1-find-f-n-x-

Question Number 27081 by abdo imad last updated on 01/Jan/18

l e t g i v e f (x) = \frac{x}{4 x^{2} - 1} f i n d f^{(n)} (x) .

Answered by prakash jain last updated on 01/Jan/18

f (x) \frac{x}{4 x^{2} - 1} = \frac{1}{4} (\frac{1}{2 x - 1} + \frac{1}{2 x + 1})

f^{(n)} (x) = \frac{1}{4} (\frac{{(- 2)}^{n} n!}{{(2 x - 1)}^{n + 1}} + \frac{{(- 2)}^{n} n!}{{(2 x + 1)}^{n + 1}})