 Hi everyone! This video will walk you through how to use your Texas Instrument TI-84 graphing calculator so as to find the derivative of a function at a specified point. This video would be for the TI-84, the TI-84 plus silver edition, color edition, any of those models that you might have. It is also understood that on your calculator you would have the current updated operating system, and they refer to as the quote-unquote pretty print. So if yours does not look like mine does, that means you might have the older operating system, which I will address as I go through. So there are two primary ways to use your graphing calculator so as to find a numerical derivative. And it's these two I will be walking you through. The one is called N-derive, which can be found on your calculator under math. The math button is in the far left column. And then number eight, you'll see it says N-derive on it. The second way is a graphical way. You'll be required to graph a function, get a good window for it, and then utilize under calc, the second trace menus. It's number six to find your derivative dy dx. So let's go to the graphing calculator and we'll walk through each of those. So this one that you're seeing is the TI-84 plus C, which is the color version. If you have the regular version that's fine. Your functions will look just like this one. So suppose I had a function and I just made one up and I put it under y equals if you want to use the same one and try it. Just a basic cubic. So let me go back to my quit screen. So we'll go and do the N-derive function first. So as I was saying earlier in the left column, you'll find a math button. So hit that and you go down to number eight. You can either scroll down and hit enter or simply hit the number eight for N-derive. And again, assuming you have the updated current operating system on your graphing calculator, it should look like this. If it does not, I have it on the other side that I can show you what you'll need to do. So this notation is really nice because it's really just like calculus notation. What they're prompting you is you're basically filling in the boxes that you see. So the first box is just simply going to be an x. That means we're finding d dx, the derivative with respect to x. Now in the second box, the one that's located in the parentheses, you have a choice. Either you can type in the function right there. Or if you happen to have it stored under y equals, as we do with our example, we can just pull up y one. So you can do either one. So I'm going to pull up y one. So the way in which you do that, of course, is with vars and then over to y vars and function and y one, because that's where mine's located. Then you just use your right arrow to hop over to the next one. You'll notice that now it says x equals. And that's where it's asking you for the x value at which you want to find the derivative. The vertical line or math symbol for such that. So really how you would read this is you're finding the derivative with respect to x of what you have under y one, such that x equals and let's do negative one. And then you just simply hit enter. And there's your answer. So it's looking like it's a pretty steep tangent line to the curve at x equals negative one if it has a slope of about 23. And you could just keep doing that for different x's over and over and over. So let me show you the graph. Again, remember we had the equation under y equals. You can just do zoom six to graph it. And again, even if you do not have the color version, this works the exact same way on the regular TI 84s, the 84 pluses, the silver additions, etc. All right, so let's go ahead and find that derivative, the slope of the tangent line at x equals negative one again. So what you're going to do is hit your second and trace. You'll notice it says calc and I'm sure you're familiar with a lot of these functions under here. We want the one down at number six, dy dx. And you'll notice at the bottom, it kind of puts your cursor someplace right in the center of the graph. You'll notice down at the bottom it's asking you for x equals whatever. So you just simply type in the x value. So I'm going to type in negative one, hit enter, and you'll notice right above it, right here, you have dy dx equals at 23.0002, which is the same answer we obtained doing it with n derive. So now again, if you happen to have the older operating system, you'll notice under the first bullet here, when you do the math eight, the n derive, you're going to be prompted with something that looks a little different than what you saw with our calculator example. You're going to have n derive and then you'll be prompted with a parenthesis. You'll get the same answer in the end, you just need to enter it differently. So the way in which you'll enter it, I have written out for you right here. The first thing that goes in the parenthesis is your equation. So again, you can either type in the actual equation, or if you happen to have it under y one or any other y equals, you can bring that up. And then it's comma x comma and the x number at which you want to find the numerical derivative. And then simply hit enter. Again, that would be for the older operating system. So hopefully this was a little help to you. Take care.