4: 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
![](gif5/eca5ad4.gif)
Do not forget to put this answer back into the exponential.
Answer