In "Japanese in MangaLand" Lesson 35, the "negative te form" and "the te form of the negative" were both introduced. And a table was showing the following:
simple | neg. -te | -te f. of the neg.
教える | 教えないで | 教えなくて
貸す | 貸さないで | 貸さなくて
But I was confused, could anyone please tell when I should use which please? Thank you!