Question

Найти производную данного выражения .

Answer 1

$[ sqrt{(1-x^2)/(1+x^2)} ]`=1/2* sqrt{(1+x^2)/(1-x^2)} *[-2x(1+x^2)-2x(1$$-x^2)]/(1+x^2)^2=1/2* sqrt{(1+x^2)/(1-x^2)} *[-2x(1+x^2+1-x^2)]/$$(1+x^2)^2=1/2* sqrt{(1+x^2)/(1-x^2)} *(-4x)/(1+x^2)^2=-2x*$$sqrt{1+x^2} /(1+x^2)* sqrt{1-x^2} =-2x/ sqrt{(1+x^2)^3}* sqrt{1-x^2} =$$-2x/(1+x^2)* sqrt{1-x^4}$