The differential operator is coming!

One day, in Mathland, you and x are walking around, talking about the weather. After a while, x² and e^x join you. The conversation moves to more small talk when, all of a sudden, 1 comes running by, screaming: "The differential operator is coming! Run for your lives!"

x and x² look around nervously and tell you they have to split. After they leave, you turn to e^x and ask what the problem was. "Oh, that's the differential operator, d/dx. When he gets close, he has to act. For 1 it's especially nasty, since he will completely vanish. And also for x and x² it's quite irritating. But for me, it's no problem; I'll just transform into my old self again." And with a 'poof', he suddenly vanishes. You hear a soft noise behind you and you turn around.

"Hi," says the differential operator. "I'm d/dy."