Y=X*根号[(1-x)/1+x]用对数求导法求的话,请问大侠该怎么求

Question

Y= X * 根号[(1-x)/1+x]用对数求导法求的话,请问大侠该怎么求

Answer 1

lny = lnx - (1/2)(ln(1-x)-ln(1+x))
两边求导有
y'/y = 1/x - (1/2)(-1/(1-x)- 1/(1+x)) =1/x + 1/((1-x)(1+x))
y'= y *( 1/x + 1/((1-x)(1+x)) )
=x * 根号[(1-x)/1+x] * ( 1/x + 1/((1-x)(1+x) )
=根号[(1-x)/1+x] * ( 1 + x/((1-x)(1+x) )