Hi, welcome to the third week of the Calculus course. Recently, we have covered concepts of limits for various entities. Sequences, single variate, and multivariate functions. Now, it's time to turn to more sophisticated and far more famous subject; derivatives. It's just a common knowledge is that Calculus course is mostly about derivative. The problem here is that most people didn't realize that it's not very tense. So anyhow the proper way to properly start to study something is to understand to why we're studying it. So imagine the following case. Assuming that I have to travel from home to work, say 100 kilometers. Well, say it takes two hours for all the way. As such, my average speed is 100 divided by 2, 50 kilometers per hour. Say the limit here is 80 kilometers per hour. It doesn't necessarily, mean that I will not get a ticket for speeding. Well, in case I was driving all the way versus same speeds which is my average speed or I'll exit blue curve on our graph. It's actually right. But in a real life it's not, in real life my 50 kilometers per hour arguments won't stand in court because as the court actually cares about whether I was driving under the limit all the way through at every point of my way and every point of time. So in order to understand whether or not I am getting a ticket, we need to introduce ourselves to concepts of instantaneous speed, the speed of change of my distance from home at every moment of time, and that's what's derivative mean. So in the following week, we are going to firstly define a derivative, understand basic arithmetic rules for it, and then move forward linear approximations with the use of derivative and derivatives of higher order. So let's begin. I'll see you in the next, in the following video.