Question 1205161
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Find (nth) derivative of f(x)= (x² + x + 1)/(x + 1)
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<pre>
{{{(x^2 + x + 1)/(x + 1)}}} = {{{(x^2+x)/(x+1)}}} + {{{1/(x+1)}}} = {{{(x*(x+1))/(x+1)}}} + {{{1/(x+1)}}} = x + {{{1/(x+1)}}}.


1-st derivative is   1{{{-1/(x+1)^2}}}.

2-nd derivative is     {{{2/(x+1)^3}}}.

3-rd derivative is     {{{-(2*3)/(x+1)^4}}}.

4-th derivative is    {{{(2*3*4)/(x+1)^5}}}.

. . . . . . . .

n-th derivative is    {{{((-1)^n*n!)/(x+1)^(n+1)}}},  where n is an integer >= 2.    <U>ANSWER</U>
</pre>

Solved.