The symbol "u'" typically represents the derivative of a function u with respect to a variable, often x. In calculus, derivatives measure how a function changes as its input changes, providing insights into the function's behavior, such as its slope or rate of change. In mathematical notation, if u is a function of x, then "u'" indicates the first derivative of u. This concept is fundamental in various fields, including physics and engineering, where understanding rates of change is crucial for analyzing motion, growth, and other dynamic systems.