The notation G'(x) represents the derivative of a function G with respect to the variable x. In calculus, the derivative measures how a function changes as its input changes. Essentially, it provides the slope of the tangent line to the curve of the function at any given point, indicating the rate of change of G at that specific value of x. Calculating G'(x) involves applying rules of differentiation, such as the power rule, product rule, or chain rule, depending on the form of G. The result can be used to analyze the behavior of the function, including identifying local maxima and minima, and understanding how G behaves over its domain.