Question

derivative of y=x.lnx-x at x=1​

Answer 1

y = x.lnx - x

dy/dx = d(x.lnx)/dx - d(x)/dx

= (d(x)/dx.lnx + d(lnx)/dx.x) -1       (product rule)

= 1.lnx + (1/x).x -1

= lnx +1 -1

= lnx

f(x) = f(1) = ln1 = 0.

Hope it helps.