The derivative refers to the rate of change, or slope, of a function. Differentiation refers to the calculation of a derivative. Derivatives are used throughout applied mathematics and science. The derivative of a function is the instantaneous rate of change of a function evaluated at each point.
The word vector comes from the Latin term vehere, to carry. In Biology, a vector is an agent which carries disease, such as a mosquito carrying infected blood from one patient to the next. In physics, a vector is a quantity which has both a magnitude and a direction associated with it. The most commonly used example of vectors in everyday life is velocity. When you drive your car, your speedometer tells you the speed of your car, but it doesn't tell you where you are going. The combination of both where you are going and how fast you are going there is your car's velocity.
The celestial coordinate system is a projection of earth's coordinate system into the celestial sphere. Being just like Earth's system it contains an "equator", lines of "latitude" and "longitude", and even poles. (Though we don't use the same words for it.) One suggestion one might have would be to just extend the Earth's latitude, longitude, and equator out into the night sky, but the Earth is constantly spinning. For the Celestial coordinates, we have to pick some fixed reference to go by.
Parallax is the apparent displacement of a foreground object with respect to a background object caused by the movement of the observer. In plain words, nearby objects seem to shift more than distant objects when you move.
The interstellar medium, which makes up ~1/3 of the visible mass of the galaxy, is almost entirely comprised of hydrogen gas. Depending on the proximity to nearby stars, it can be either molecular (H2), atomic (HI), or ionized (HII). The next most abundant element is helium. That's pretty much it. In fact, many astronomers refer to elements in space as hydrogen, helium, and "metals". Those metals, which make up ~1% of the mass of the ISM are primarily composed of small iron particles and silicate and carbon soot. This soot, or "dust" as it is generally called, while a tiny fraction of the galaxy, plays an extremely important role both in how we observe the heavens, and on our life on this planet.
Charles Darwin's theory of natural selection was the first plausible mechanism to explain the change of species over time, however, in it's original form it did not explain how new traits could form, or how traits that had formed could be passed on to successive generations. The rise in modern genetics helped to modify biologists understanding of evolution by attributing the origin of new traits in a species to random genetic processes of mutation and sexual recombination, with the survivability of species with the new traits subject to natural selection. This combination of random mutation and natural selection is often referred to as Neodarwinism.