The notation "g'(x)" represents the derivative of a function g at a specific point x. The derivative measures how the function's output changes as the input changes, essentially providing the slope of the tangent line to the graph of g at that point. This concept is fundamental in calculus and helps in understanding rates of change. In practical terms, if g describes a physical quantity, such as distance over time, then g'(x) indicates the speed at which that quantity is changing at the moment x. Derivatives are widely used in various fields, including physics, engineering, and economics, to analyze trends and make predictions.