Hello, I welcome you to my channel mate with its objective [Music] Hello, in this exercise we are going to work with introductory aspects related to the topic of functions of several variables. At some points, I am going to ask you to stop the video so that you can reflect on the questions posed and write down your answers. When you resume the video, several of the answers will appear so that you can compare them with those that you are not sure. Don't worry if they don't match, you will surely have good reasons for having done it that way and it will be enriching to share them in the group session. Do you remember what a function is from a mathematical perspective? What are its main characteristics? You can stop the video now, based on your previous reflections, how could a function of one variable be expressed, that is, what would be a general representation of a function of one variable? You can stop the video now. This is a possible answer that is equal to fx. This is a general expression that is used to identify what the dependent variable is in this case yes, and what is the independent variable, in this case x, then how is a function of two variables defined? You can stop the video now. This is a possible answer. Z is a function of x, comma, and the dependent variable z. and the independent variables x finally how is a function of several variables defined you can stop the video now this expression is already a function of x 1 x 2 up to x n we can see in this expression that n is a natural number that can contain any number of variables 1 2 10 50 etcetera of something that this is a possibility it is not practical to use different literals to identify the independent variables as was the case with the function of two variables xy instead the same literal is used which in this case is x but subscripts are used to indicate that x1 is a different variable from x2 and the rest of the variables present if we take into account that this expression contains all the functions of n variables then we could put this other proposal which is a function of x1 and x2 these two expressions are equivalent only here the same literal is being used to identify the independent variables but using subscripts if you have questions with additional comments write them down to discuss them as a group that 's all for now thank you for your attention until next time