Processing Math: Done

Aus Online Mathematik Brückenkurs 2

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

xsinx=x2(sinx)x−sinx(x)=x2cosxx−sinx1=xcosx−x2sinx.

It is also possible to see the expression as a product of sinx and 1x, and to use the product rule,

sinxx1=(sinx)x1+sinxx1=cosxx1+sinx−1x2=xcosx−x2sinx

where we have used

x1=x−1=(−1)x−1−1=−1x−2=−1x2.