用对数求导,(1-x/1+x²)的开方用对数求导,y=x(1-x/1+x²)的开二次方y=x〔(1-x/1+x²)的开二次方〕

Question

用对数求导,(1-x/1+x²)的开方
用对数求导,
y=x (1-x/1+x²)的开二次方
y=x 〔(1-x/1+x²)的开二次方〕

Answer 1

y=x (1-x/1+x²)的开二次方
lny=1[lnx+1/2*ln(1-x/1+x^2)]=lnx+1/2*ln(1-x)-1/2*ln(1+x^2)
求导
y'/y=1/x-1/2*(1/1-x)-x/(1+x^2)=1/x+1/2(x-1)-x/(1+x^2)
y'=[1/x+1/2(x-1)-x/(1+x^2)]*x (1-x/1+x²)的开二次方