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Hello again, Tom from everystepcalculus.com. Difference quotient, regarding the square roots. And let’s do it. Index 8 you come to my menu here. I’m going to scroll down to what’s asking your test problem. Do the difference quotient to find the definition of derivative. So we scroll down here to difference quotient. Press ENTER and we under the program. Always write the formula on your paper first okay. Sometimes Delta X might be used in you from your professor for character H. So do that. Any time you see an H you’re going to put delta X okay. And then you’re going to have look at my program and change the character as you go through it. Enter the function here you have to press alpha first and enter my programs. And so the function we’re going to enter is 7 times second which is the time sign, which is the square root sign X + 13. X + 13 closed off at parenthesis. Press ENTER, here’s a few minute I will show you that so you can change in case you made a mistake it’s what we entered so that’s cool. It’s busy loading the program. And we’re going to rendering X + H for every one of these X’s in the function all over H. we get rid of the radicals by squaring them. Here’s the denominator with H. we’re going to multiply the same thing up here at the top which you can do equals 1. So you can multiply whatever and then whatever you think up on the bottom of the denominator and put it in the top. Right now we’re going to add the radicals and put in the top of the cube. Which gets rid of these okay. When you multiply radical times of radical. It becomes a not radical okay. You want to find out if we’ve gotten rid of the radicals here. No problem, you still have the radicals in the bottom of course. Expand the numerator, turns out to be this. Combined the numerator turns up by 7H. We divide the H out becomes 7 and then we have this remaining in the denominator okay. Now there’s an H here. So as H approaches 0 which is the definition of, or the rule when you’re dealing with limits. As H approaches in this case. It is approaching 0 so what an equals 0. The H comes out. And we have X + 13 plus square root of X + 13. So we get two times the square root X + 13 which is the answer is something denominator okay. So this is all basic algebra I’m in this very difficult who knows elder were this good. But I mean you can study it for weeks and know it. But I mean who wants to study it. Who needs to study it? It’s complete waste of time. So use my programs and pass calculus okay. so have a good one. everystepcalculus.com

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Hello Tom, from everystepcalculus.com from everstepphysics.com. The difference quotient is what we’re going to do here. And I need to do one more because the square roots are kind of difficult because you have to get rid of the radical signs. And get of radical. You multiply times a radical and our radical squared is turns out to be whatever is inside the radical okay. So I’m going to show you kind of a very simple one here. So maybe you can learn this better or to understand it better. We’re going to scroll down here to difference quotient. Here’s the form you write that on your paper all the time we were to do that. Enter the function. And to press alpha first, alpha second. Time sign is a square root sign of X. And we’re going to this close up the prices. So in the front are going to add X + H, to every X in the function. I say it’s okay, it gives a chance to change it in case you may never stay put. And we’re loading the program here. Again the formula. So we’re going to put X + H here in the radical and we’re going to subtract the function. Visual function which is the funding divided by H. To get rid of radicals you need to multiply it. Somehow the radicals, times itself. Okay spire radical you get what’s inside the parentheses and the radical. So we’re going to here’s, the radicals here we’re going to have to put that in the denominator. Because you can’t just do it in the numerator you have to do the denominator also which actually equals 1. It’s multiplying x 1. So we look at what radicals we need to get rid of. We need to multiply that times that. And there is we’re doing that we’re putting in the denominator also okay. When you do that you get what’s inside the radical which is X + H – X okay. And we have H down here and we still have the radicals down here. We have to have that. In algebra expand it, you get this up in the numerator. We get H in the numerator and divide out the H, you get a 1. Still have an H here. As H approaches 0 when you’re taking the limit of a function. In this case that equals 0 so X + 0 is X. So you get two square root X on the bottom. Sorry this is not over here further but I have to make room in cases are extremely hard function and they take up the whole line down here okay. So you get the idea and so the answer is two times the root of X okay. This is the derivative the retribution function. Pretty neat everystepcalculus.com. Don’t waste time. Go to my programs buy them. There cheap for what you get here. I’ve studied years in this crap to help you pass calculus and of course you can buy my programs and pass calculus. So have a good one okay. everystepcalculus.com

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