Question

求函数y=((1+x)/(1-X))^1/2的导数

Answer 1

y=((1+x)/(1-x))^1/2

y'=1/2((1+x)/(1-x))^(-1/2)*((1+x)/(1-x))'

=1/2((1+x)/(1-x))^(-1/2)*((1+x)'(1-x)-(1+x)(1-x)')/(1-x)^2

=1/2(1+x)^(-1/2)/(1-x)^(-1/2+2)*(1*(1-x)-(1+x)(-1))

=1/[2(1+x)^(1/2)(1-x)^(3/2)]*(1-x+1+x)

=1/[2(1+x)^(1/2)(1-x)^(3/2)]*2

=1/[(1+x)^(1/2)(1-x)^(3/2)]