Remember back in week one? I introduced the idea of calculus and that we would need it later on to do price optimization. Well, we have now come to that point. Now calculus you might know is, one of the great intellectual achievements of mankind. So if you can spend some time learning more calculus, have at it. I think it is a wonderful way to spend your time. Today I am going to take a more limited approach, we are going to learn how to take a derivative. Some of you may know this already. If you don't, I will teach it to you and this is what you have to do the price optimization that I will be doing momentarily. Now, I am going to write down a function and then in particular, I am going to write down Y equals 6x at its most most basic level. What a derivative is, is a measurement of how quickly a function changes relative to the variable. In this case, the variable is x. So you might look at that and say well, if x goes up by one, how much will y go up by. I think the answer is pretty clear, right? The answer is six. Every time x goes up by one Y goes up by 6, that is the rate of change of the function. So if I formalize that, I can formalize that by taking the derivative of the function. And this little squiggly thing out in front of the Y, if you've never seen that before, that's just a derivative sign. And I'm saying, I'm taking the derivative of y with respect to x. And it turns out, that that is equal to that six. How do I get that? Well, there's a little rule in taking a derivative. And that says, when you're taking a derivative and you've got a constant, that six is a constant and you've got a variable. That x is a variable. Then taking a derivative with respect to that variable is just equal to the constant, okay. So, the derivative of y with respect to 6x is just six. If it were 8x there, it would be eight. All right, so if you understand that, the next thing I'm about to tell you is very straightforward. Suppose you have a situation where y = Three and you ask the question, what's the derivative of y with respect to x. Well, there's no x in the equation. That function doesn't change as x changes, because there's no x there. So the derivative of y with respect to x is zero. And in fact, the derivative of y equal to any constant, whether that's four, or five, or 17, is simply going to be equal to zero. Now, there's one other thing I've got to show you. This is the only thing that's even slightly tricky, but I'll walk you through it. Suppose you have a little more complicated function here. Lets say you have y equals 2x to the 3rd power and you ask the question what is the derivative of y with respect to x. Well, here's how you do that. Remember, you're measuring the rate of change of a function and mathematically, here's how you handle something like that. You take the number that send the exponent, right? The power number sitting out there and you multiply it by the constant upfront. So in this case, we'd have three times two, you insert the x and then, you subtract one from the exponent, so it's 3- 1. So in this case, the derivative of y with respect to x is 6x squared. So again, you just take the exponent, multiply it by the constant out front and subtract one from that exponent and you're done. And that's really all you need to know to do the price optimization coming up.