Why its said that derivation is reverse of antiderivatives?

Answer 1

It is said that derivation is reverse of antiderivation because that is the terminology.

If you have a function f(x), then the derivative d/dx f(x) is the slope of the function f(x) at each x. This derivative could be called g(x). Sometimes it is called f'(x), but lets call it g(x).

Now, start over...

If you have a function g(x), then the antiderivative is a function f(x) such that the derivative d/dx f(x) is g(x). This may sound like circular definition, but it is not...

If the derivative of f(x) is g(x), then the antiderivative of g(x) is f(x). Technically, the antiderivative of g(x) is f(x) + C, where C is any constant. This is true because the derivative of a constant C is zero.

Now - terminology.

Taking the derivative is the same thing as derivation.

Taking the antiderivative is the same thing as reverse derivation.

Taking the deriviative is the same thing as reverse antiderivation.

Antiderivation is also called integration and that is the next topic after derivation. They are simply the reverse processes of each other.