# Applications of the Derivative

The derivative of a function of a variable x is a function that satisfies the following properties: Let f be the function whose value at x = a is "f(a)". The derivative of a constant function is zero. The derivative of a constant function is a constant function. The derivative of a linear function is a linear function. The derivative of the square function is the square function. Note that the above definition of the derivative is not well-defined if the function is not defined at the origin.