Lösung 1.2:1d

Aus Online Mathematik Brückenkurs 2

Version vom 14:23, 16. Sep. 2008

We have a quotient between sinx and x, and therefore one way to differentiate the expression is to use the quotient rule:

xsinx=x2sinxx−sinxx=x2cosxx−sinx1=xcosx−x2sinx

It is also possible to see the expression as a product of

sinx and x1, and to use the product rule,

sinxx1=sinxx1+sinxx1=cosxx1+sinx−1x2=xcosx−x2sinx

where we have used

x1=x−1=−1x−1−1=−1x−2=−1x2