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Lösung 1.2:1d

(Unterschied zwischen Versionen)

Version vom 10:02, 11. Mär. 2009

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)

=x2cosx

x−sinx

1=xcosx−x2sinx.

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

sinx

=(sinx)

x1+sinx

=cosx

x1+sinx

−1x2

=xcosx−x2sinx

where we have used

x−1

=(−1)x−1−1=−1

x−2=−1x2.