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Lösung 1.2:2c

Aus Online Mathematik Brückenkurs 2

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When we see this expression, we should think "root of something",


 


and in order to differentiate it, we should first differentiate the outer function , "the root of", with respect to its argument and, after that, multiply by the derivative of the inner functional expression

=cosx,


ddxcosx=12cosxcosx ,

where we have used the differentiation rule


ddxx=ddxx12=21x211=21x21=12x.

Thus, we obtain


ddxcosx=12cosxsinx=sinx2cosx