Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Lösung 1.2:1f

Aus Online Mathematik Brückenkurs 2

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 1.2:1f moved to Solution 1.2:1f: Robot: moved page)

Version vom 14:23, 16. Sep. 2008

In this case, we have a slightly more complicated expression, but if we focus on the expression's outer form, we have essentially "something divided by sinx ". As a first step, we therefore use the quotient rule,


sinxxlnx=sinx2xlnxsinx−xlnxsinx 


We can, in turn, differentiate the expression xlnx by using the product rule:


xlnx=xlnx+xlnx=1lnx+xx1=lnx+1


All in all, we thus obtain


sinxxlnx=sinx2lnx+1sinx−xlnxcosx=sinxlnx+1−sin2xxlnxcosx

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