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

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Answer 1 · 2015-11-14T03:25:58

$ln(x)$ , through the product rule

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

$f'(x)=d/(dx)[x]*ln(x)+x*d/(dx)[ln(x)]-1$
{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 $1/x$ .}

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

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