differentiation

I hear lots of people using the word "derive" to mean "take the derivative of" or "differentiate". I personally don't like this term.

While I cannot definitively say that the usage of "derive" to mean "differentiate" is incorrect, I can definitely say I have never seen a textbook or a teacher use "derive" to mean "dy/dx".

I feel the need to differentiate (haw haw) between the two, and explain the usage of the two in mathematics.

Differentiate
This means to take the derivative of. This means dy/dx. This means "kick the power down, subtract one from the power".

Derive
This means "prove" or "find". This means if "a + b = c", then we can derive that "a = c - b". If a question says "derive this function", it will always mean "look at the diagram and the information given, and use LHS = RHS to prove that the function given is correct". It will never mean "differentiate this function".