How do you differentiate ##f(x)=xlnx-x##?
February 20th, 2023
##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)##
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