Differentiate the following functions with respect to x :
x+ex1+log x
By Using quotient rule, we have
ddx(x+ex1+log x)
=(1+log x)ddx(x+ex)−(x+ex)ddx(1+log x)(1+log x)2=(1+log x)(1+ex)−(x+ex)×ddx(1+log x)2
=x(1+log x+ex+exlog x)−x−exx(1+log x)2=x+xlog x+xex+xexlog x−x−exx(1+log x)2
=x log x(1+ex)−ex(1−x)x(1+log x)2