Производная y=arctg корень((x-1)/(x+1))

Question

Производная y=arctg корень((x-1)/(x+1))

Answer 1

Y`=1:(1+(√[(x-1)/(x+1)])²)*1/2√[(x+1)/(x-1)]=1:(1+(x-1)/(x+1))*1/2√[(x+1)/(x-1)]=
1:[(x-1+x+1)/(x+1)]*1/2√[(x+1)/(x-1)]=1:2x/(x+1)*1/2√[(x+1)/(x-1)]=
=(x+1)/2x *1/2√[(x+1)/(x-1)]=√(x+1)³/[4x√(x-1)]