Raw Transcript Hello, everyone. Tom from everystepcalculus.com and everystepphysics.com. I’m gonna do a a definition of the derivative or difference quotient problem right now. et’s do it. Index 8 to get to my menu. Scroll down to definition of a derivative. There it is there. I gave you a little bit of help in case your professor does some tricks change of X instead H. There’s all kind of tricks and this is one of the most nonsensical things I’ve ever seen in calculus. It’s all nonsense but.. I’m going to choose number two, here. For a square root function. I’m going to enter the function. You have to press Alpha before you enter anything into these entry lines. Alpha, going to use the square root second square root of X minus 4, close off the parentheses. And I say it’s okay I give you a chance to change it in case you make a mistake. Here’s the formula. And remember, you’re replacing X plus H for every X in the function. And then in the case of square roots, you’re using the difference squares to get rid of the radical signs. So we’re multiplying it times the plus of the same thing which makes those squares. I’ll show you that in the next one, here. So they become squares and when you square a square root, you get what’s inside the square root. Here it is. And in the bottom, of course H, you do the same thing because they’re really taking the numerator and denominator exactly the same thing which you have to do So you don’t change the function. And then on the top, we multiply it all together. And you come up with H on the top, these H’s cancel. Becomes one and now we’re gonna when H equals 0, then we apply that to this down here which cleans that up and makes it the same thing. Two of each right here. So that’s where the two comes into it. Here’s the answer one over two times square root of x minus 4. As usual, calculus makes a big big deal about this when
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