The process of computing f'(x) for a given function f(x) is called differentiation.
The concept of derivative in economics are described by the adjective "marginal."
That, if C(x) is a cost function (the cost of producing x units of a commodity), then the derivative C'(x) is called the marginal cost function. The derivative P'(x) of a profit function P(x) is called the marginal profit function; the derivative of a revenue function is called the marginal revenue function.