The expression "f'(g(x)) * g'(x)" represents the chain rule in calculus, which is a method for finding the derivative of a composite function. Here, f is a function that takes another function g(x) as its input. The derivative of f with respect to its input, evaluated at g(x), is denoted as f'(g(x)). The term g'(x) represents the derivative of the function g with respect to x. By multiplying these two derivatives together, we can determine how the composite function changes with respect to x. This is essential for understanding the behavior of complex functions in calculus.