Question

умоляю найдите производную y=log x по основанию (х+1)

Answer 1

y=log(x+1)x=lnx/ln(x+1)
y`=[ln(x+1)/x-lnx/(x+1)]/ln²(x+1)=ln(x+1)/[xln²(x+1)]-lnx/[(x+1)ln²(x+1)]=
=1/[xln(x+1)]-lnx/(x+1)ln²(x+1)]