#f(x)=sqrt(1-x)/sqrt(1+x)#
By applying quotient rule,
Let #u=sqrt(1-x)# and #v=sqrt(1+x)# #f'(x)=(u'v-v'u)//v^2# #f'(x)={1/2root(-1/2)(1-x)*sqrt(1+x)-1/2root(-1/2)(1+x)*sqrt(1-x)}/(1+x)# #f'(x)=1/2{(sqrt(1+x)/sqrt(1-x))-(sqrt(1-x)/sqrt(1+x)}//(1+x)# #f'(x)=1/2{1+x-1+x}/((1+x)sqrt(1-x^2))# #f'(x)=x/((1+x)sqrt(1-x^2))#