Right. There are a lot of comments along the lines of "Duhhh, that's the point of calculus" here. But you know what? Screw that. People learn when people learn, and discovering it for yourself is a lot cooler than someone telling you about it, especially if it's related to investigating something you care about.

I can't tell you the number of 'trivial' math facts that I have (re)discovered because they were in the context of something I cared deeply about.

The point isn't to remember D_x is a linear operator--math isn't about memorization. It's about understanding the context where this is a useful fact and knowing how to figure it out.

Learn it in Calc I and you can half-heartedly reference it (...isn't differentiation linear? I feel like I remember that from senior year of high school...).

Figure it out on your own and you own it for life.

Post it to the internet and you get ridiculed and mocked for it so that you wish you could forget it.