I take this to be y = xex.
Proceeding formally (ie, without regard to restrictions on the domain of ln x):
- Take natural logarithms of 'both sides' of above equation: ln y = ln x + x
- Implicit differentiation: y'/y = 1/x + 1
- Multiply both sides by y: y' = y ( 1/x + 1 )
- Replace y by its definition as a function: y' = xex ( 1/x + 1 ).
