How do you differentiate ##f(x)=xlnx-x##?

##ln(x)##, through the

##f'(x)=d/(dx)[xln(x)]-d/(dx)[x]##

##f'(x)=d/(dx)[x]*ln(x)+x*d/(dx)[ln(x)]-1## {Product Rule: ##d/(dx)[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)##}

##f'(x)=1*ln(x)+x*1/x-1## {Remember that the derivate of ##ln(x)## is ##1/x##.}

##color(red)(f'(x)=ln(x))cancel(+x/x)cancel(-1)##