(1,0) are (s,t)-coordinates, whereas (-7,3) are the corresponding (u,v)-coordinates.PsychonautQQ said:it doesn't matter that the coordinates change from (-7,3) to (1,0)?? I confused X_x
A partial derivative is a mathematical concept that represents the rate of change of a function with respect to one of its variables, holding all other variables constant. It is a fundamental tool in multivariable calculus and is used to study how a function changes in different directions.
Partial derivatives are important because they allow us to analyze how a function changes with respect to each of its variables separately. This is especially useful in fields such as physics and engineering, where many variables are involved in a system and their relationships need to be understood.
A partial derivative problem can be considered "crazy" if it involves complex functions, multiple variables, and intricate relationships between them. These types of problems require a deep understanding of the concepts and techniques of partial derivatives, making them challenging and often time-consuming to solve.
The key to approaching a crazy partial derivative problem is to break it down into smaller, more manageable parts. Identify the variables involved, their relationships, and any known values or constraints. Then, use the rules of partial derivatives to find the partial derivatives for each variable and combine them to solve the problem.
Partial derivatives have numerous real-world applications, including in physics, economics, engineering, and statistics. For example, they are used to study the rate of change of temperature in a room, the optimal production levels for a business, the behavior of a chemical reaction, and the risk of a stock portfolio. They are also essential in optimization problems, where the goal is to find the maximum or minimum of a function.