If you're going to learn one opposition, I'd say a derivative is a specific instance or product of the process of derivation, but there are exceptions to this explanation, and the distinction often depends on the field/context in question. Derivative can also be an adjective, whereas derivation is always a noun. ** In general, I'd recommend learning derivative's most common noun and adjective meanings and only worry about derivation if it matters to you because of a specific context (e.g. if you're a mathematician or something). Derivative is the much more useful word, in my opinion. I can't think of a single time I've used derivation in my daily life, but derivative probably comes up once a month—I'd consider it an important word for an advanced learner. Some complications for each, just to show how diverse they can be: Derivation (In gunnery) The deviation of a projectile from its normal course due to its form, motion, the resistance of the air, or wind; spec. the constant inclination of a projectile to the right due to the right-hand spin imparted by the rifling; drift. (In medicine) The withdrawal of inflammation or morbid humour from a diseased part of the body, by blistering, cupping or other means. Derivative (as a noun): (In music) A chord derived from a fundamental chord, esp. by inversion. (In medicine) A method or agent that produces derivation And in math, they both have specific meanings: http://people.math.harvard.edu/~elkies/M250.04/deriv.html

Derivation is the PROCESS of making a derivative. In math: you can find the slope of a line tangent to the curve y=x^2 by performing derivation on the equation. The equation's derivative is 2x+c. In language: Bob just learned the derivation of the word "comfortable". He learned that "comfortable" is a derivative of the Latin words for "with strength". In manufacturing: The derivation of most modern hydrogen supplies involves the use of water and methane. Most modern hydrogen supplies are derivatives of water and methane.

(I've switched this to an answer rather than a comment so others can agree or disagree with me.)