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Lösung 1.2:1c

Aus Online Mathematik Brückenkurs 2

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K (Lösning 1.2:1c moved to Solution 1.2:1c: Robot: moved page)

Version vom 14:22, 16. Sep. 2008

The expression is a quotient of two polynomials, x2+1 and x+1, and we therefore use the quotient rule for differentiation:


x+1x2+1=x+12x2+1x+1−x2+1x+1=x+122xx+1−x2+11=x+122x2+2x−x2−1=x+12x2+2x−1


NOTE: it is possible to rewrite the numerator by completing the square,


x2+2x−1=x+12−12−1=x+12−2 


and then the answer can be written as


x+12x2+2x−1=x+12x+12−2=1−2x+12

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.2:1c“