SOLUTION: Find (nth) derivative of f(x)= (x² + x + 1)/(x + 1)

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Question 1205161: Find (nth) derivative of f(x)= (x² + x + 1)/(x + 1)
Answer by ikleyn(52787) About Me  (Show Source):
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Find (nth) derivative of f(x)= (x² + x + 1)/(x + 1)
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%28x%5E2+%2B+x+%2B+1%29%2F%28x+%2B+1%29 = %28x%5E2%2Bx%29%2F%28x%2B1%29 + 1%2F%28x%2B1%29 = %28x%2A%28x%2B1%29%29%2F%28x%2B1%29 + 1%2F%28x%2B1%29 = x + 1%2F%28x%2B1%29.


1-st derivative is   1-1%2F%28x%2B1%29%5E2.

2-nd derivative is     2%2F%28x%2B1%29%5E3.

3-rd derivative is     -%282%2A3%29%2F%28x%2B1%29%5E4.

4-th derivative is    %282%2A3%2A4%29%2F%28x%2B1%29%5E5.

. . . . . . . .

n-th derivative is    %28%28-1%29%5En%2An%21%29%2F%28x%2B1%29%5E%28n%2B1%29,  where n is an integer >= 2.    ANSWER

Solved.