Lösung 1.2:2f

Aus Online Mathematik Brückenkurs 2

The entire expression is made up of several levels,

cos1−x 

and when we differentiate we go from the outside inwards. In the first stage, we consider the expression as "cos of something",

cos

and differentiate this using the chain rule:

ddxcos1−x=−sin1−x1−x 

In the next differentiation, we have "the root of something",

1−x=121−x1−x 

where we have used the differentiation rule,

ddxx=12x 

for the outer derivative.

The whole differentiation in one go becomes:

ddxcos1−x=−sin1−xddx1−x=−sin1−x121−xddx1−x=−sin1−x121−x−1=21−xsin1−x