Final answer:
Common notations used to denote the derivative of y = f(x) include dy/dx, f'(x), Df(x), and d/dx(f(x)), each serving as a different way to express the rate of change of y with respect to x.
Step-by-step explanation:
The student's question about the different notations used to denote the derivative of a function y = f(x) can be answered by listing some common alternative notations. The standard notation for the derivative of a function is given by dy/dx, which represents the rate of change of the dependent variable y with respect to the independent variable x. Another commonly used notation is f'(x), which is known as Lagrange's notation. Similarly, Df(x) is another notation that is used occasionally, often referred to as Euler's notation. Lastly, the notation d/dx(f(x)) explicitly states that the derivative is being taken of the function f(x) with respect to x.