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I hope this explanation will help you. Differentiation is a fundamental concept in calculus. It's the process of finding the rate at which a function changes. In simpler terms, it tells you how a quantity (usually represented as a function) is changing at a specific point. Imagine you have a function that describes the position of a car over time. Differentiation would help you determine the car's speed at a particular moment. On the other hand, a derivative is the result of differentiation. When you perform differentiation on a function, you get another function called its derivative. This new function represents the rate of change of the original function. So, if you differentiate the position function of the car, you'll get a new function representing its speed. In summary, differentiation is the process of finding rates of change, while a derivative is the mathematical expression or function that represents that rate of change. Think of differentiation as the action, and a derivative as the outcome.

Fundamental particles like electrons tend to be points. But they also have a wave nature. The vertical lines are a result of the slits being vertical. If you have diffraction through a circular hole, you get a bright dot surrounded by concentric rings http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html https://en.m.wikipedia.org/wiki/Airy_disk

A single photon or electron passes through both slits and interferes with itself resulting in the interference pattern.

After considering the last two comments, by @Janus and @Markus Hanke, I've realized that my attempt has failed. The spatial distance in the rest frame between the two measurement events has to be accounted for as well. Thank you.

Neither photons nor electrons are spherical.

Total internal reflection, by the look of it. https://www.bbc.co.uk/bitesize/guides/zctmh39/revision/1

Please, I have seen that a million times. Let me explain: Einstein's proof said that if you split a right triangle, both of the pieces (A^2 and b^2) would make c^2. Now if you do my proof, and einsteins proof, you will find that the triangles are the same size