what is the difference between derivative and differentiation?

Question

I want to know more about what is the difference， both in single variable and multivariable， I want to know about the general definition if there is one. I will appreciate it if someone can help me!! thx!!

Answer 1

A derivative is what you get as a result of differentiation. This is more a matter of language than mathematics. It's the same as the difference between 'product' and 'production', one is process, the other is the result of that process.

Answer 2

Derivative at point $x$ is the current name for the rate of variation of a function at point $x$. It was once called differential coefficient and is still written $\frac {dy}{dx}$ where $d$ means a small variation (a small difference).

Differentiation is the process of finding a function $f'$, called the derivative of $f$, which describes this rate of variation for any point $x$. E.g. the differentiation of $f(x) = 2x^4+5$ results in the derivative $f'(x) = 6x^3$.

If the function can be described by a curve, then the rate of variation (the derivative) at point $x$ is the slope of the tangent at point $x$.