Solve d/dx x(ln(x)-1)

I had:
=d/dx xln(x) - d/dx 1
=d/dx ln(x)^x
=x^(-x-1) [and this is wrong]

Can someone show me the correct answer and working please?

it looks like you are taking the derivative of

f(x) = x[ln(x) - 1]

using the product rule I get:

f'(x) = x(1/x) + [ln(x)-1](1)
= 1 + ln(x) - 1
= ln(x)