Hi and welcome to module three of our course. Today we're going to start talking about a derivative. Now, that may sound sort of scary, but really it's just when you think about maybe you're going up a hill, right. How steep is that hill? Well, we want to look at the slope of that line, right. And so if I look at a slope, how could I tell you how high that is? Really what I want is to get the slope of that line. We call that the tangent line, right. So at any point that line, the curve we're looking at has a slope. And we're going to define that as the slope of the line that is tangent to that curve, means it just touches it at one point. Well, we try to get a formula for that. And so if we look at this curve blown up, say I take a little piece of it. Suppose I said, okay, well, if I took the slope of that line, that's kind of close, right, that's close to the slope of the tangent. If I took a point a little closer to this one, then I would have that line. And that's getting closer to the slope of that line. So what we say, is that the slope of that line right there, if we get close enough, then that's the slope of our curve. So, if we took let's just say any two points and let's say this is our point X. And then on y axis, this would be our point F of X, right. And if we go over a little ways from X, let's say we go over h amount, right, then that is X plus H. And the height there would be F of X plus H, right. The curve the value of the point of the line of the function at that point X plus H. So I could take the slope of that line, right. We know the slope of the line is the difference of the Ys, which would be F of X plus H modest F of X over the difference of the Xs, which is F of X plus H minus F of X divided by H, right. Because the X modesty X cancels. Okay, so that is the slope of the secret line. And what we do is we say that the slope of the curve at a point and we call that f prime of X or the derivative of F X or the rate of change of F and X. And we say as this distance right here gets closer and closer and smaller and smaller. So instead of being here, it's like here here and as it goes to zero, that's the slope I want. So what we say is the limit as this distance gets really small of this secret line, slope. That is what I want to consider the slope of the tangent line and that is my derivative. So there is the definition of the derivative of the function F at the point X. When we come back in our next section, we will compute this for a couple of simple functions.