1: If you change it into a ratio by moving x² + x, you will end up with (x² + x)⁻¹ in the numerator, and derivative of this expression is not really nice. However, if you look one step back, you will see that the infinity came in the form of a nicer power x², while the expression (1 + 1/x) causes no troubles at infinity, so it can be handled separately.

Thus it is better to do

Do not forget to put this answer back into the exponential.

Answer