Question

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

Answer 1

`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)`