Производная y=arctg корень((x-1)/(x+1)) - вопрос №577053611 от 1аук7 16.05.2022 10:47

Question

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

1аук7 · Answer

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)]