The rate of change in the value of a function is useful to study the behavior of a function. This change in y for a unit change in x is referred to as the derivative of y with respect to x. In finance and economics, the rate of change is called marginal or incremental. For example, the marginal cost of capital is the rate of change of the total cost of capital per unit change in the new capital raised.
The idea of the deravative as the rate of change of the function at a fixed point has a geometrical foundation. The slope of the tangent to the function at a point equals the derivative at that point.
The derivative is usually denoted by d/dx of f(x) or df/dx . It may be noted that the derivative itself is a function, and the value of the derivative depends upon where it is evaluated.
The derivative of a function f(x) at point 'a' is defined as:
The process of getting the derivatives is called 'differentiating' a function.