Use this for solving problem cases, where the limit on the right side exists or is +-infinity. These are problem Cases.
This is L’Hospital rule, used for the problem cases above.
This is how to rearrange your limits so you can use L’Hospital’s rule and still find the limit even though it has an indeterminate form. The situations are: Indeterminate quotient, Indeterminate product, Indeterminate difference and indeterminate powers.
Also, a note on derivatives and the chain rule. This is what you do with constants. Including e, which is a constant.