Processing Math: Done

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 "cosine of something",

cos

and differentiate this using the chain rule,

ddxcos1−x=−sin1−x1−x.

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

1−x=121−x(1−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−xddx(1−x)=−sin1−x121−x(−1)=21−xsin1−x.