Question

what is derivation ?

Answer 1

the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's instantaneous velocity.

Answer 2

That is a great question. I am sorry to say that a derivative has many interpretations that depend mostly on the context. Most often you will hear definitions that deal with the geometric interpretation called the tangent of a function as the increments of a denominator of some ratio becomes very very small.
Yet a derivative is simply something that is "extracted from or derived from" something else. An average is actually a derivative, but is not described as one to avoid confusion in mathematical communication. A quick example would be x-y graph, you might know that the formula of a line is y=mx +b, where M is the slope or change-in-y/change-in-x. Well M is a derivative because it is answering the question "What is the behavior of y in respect to x?"

You see a derivative is anything that can be extracted to answer a specific question.

Answer 3

To add a little more detail to the explanation when the two above, who did a very good job, mention how much something changes with respect to it's input or how much one variable changes with respect to another variable it is talking about instantaneous change. So how much say y changes with respect to x as the change in x gets infinitely close to zero ( so very very very close to 0 so 0.000000000000001 for example).
To give a real world example it is used to get a velocity function from position function. So the INSTANTANEOUS change in position with respect to time gives you the velocity. I hope this helps.
As mentioned above, its definition is contextual so this is only the strict calculus definition.