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

1 Answer

Nov 14, 2015

#ln(x)#, through the product rule

Explanation:

#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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