y=(1+logx)/(1-logx)如何求导求解(dy/dx)log以10为底

Question

y=(1+log x)/(1-logx) 如何求导 求解(dy/dx)
log 以10为底

Answer 1

不知你的底数是多少
假设是a
则y'={[1+loga(x)]'[1-loga(x)]-[1+loga(x)][1-loga(x)]'}/[1-loga(x)]²
={1/(xlna)*[1-loga(x)]-[1+loga(x)][-1/(xlna)]}/[1-loga(x)]²
=[1/(xlna)-loga(x)/(xlna)+1/(xlna)+loga(x)/(xlna)]/[1-loga(x)]²
=2/{(xlna)[1-loga(x)]²}
所以dy/dx=2/{(xlna)[1-loga(x)]²}