Processing Math: Done

Aus Online Mathematik Brückenkurs 2

The outer function in the expression is "the root of something",

x−1x+1 

and differentiating with the chain rule gives

ddxx−1x+1=12x−1x+1x−1x+1 

We establish the inner derivative by using the quotient rule,

ddxx−1x+1=12x−1x+1x−12x+1x−1−x+1x−1=12x−1x+1x−121x−1−x+11=12x−1x+1−2x−12=−x+1x−11x−12=−1x−132x+1

where we have used the simplification

x−1x−12=x−12x−112=x−121−2=x−1−23=1x−123