document.write( "Question 1205161: Find (nth) derivative of f(x)= (x² + x + 1)/(x + 1) \n" ); document.write( "
Algebra.Com's Answer #841814 by ikleyn(52790)\"\" \"About 
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\n" ); document.write( "Find (nth) derivative of f(x)= (x² + x + 1)/(x + 1)
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document.write( "\"%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\".\r\n" );
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document.write( "1-st derivative is   1\"-1%2F%28x%2B1%29%5E2\".\r\n" );
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document.write( "2-nd derivative is     \"2%2F%28x%2B1%29%5E3\".\r\n" );
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document.write( "3-rd derivative is     \"-%282%2A3%29%2F%28x%2B1%29%5E4\".\r\n" );
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document.write( "4-th derivative is    \"%282%2A3%2A4%29%2F%28x%2B1%29%5E5\".\r\n" );
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document.write( ". . . . . . . .\r\n" );
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document.write( "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\r\n" );
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