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Campbell University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

00:33

Dungarsinh P.

If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$

00:50

Masoumeh A.

0:00

Felicia S.

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mhm. So whoa, you look at this function and you say, Oh, my gosh. I have to take the derivative with respect, X. And then why of this mess? Well, let me take the derivative with respect to X first. What do I get derivative of X y, With respect to X is just gonna be why and then Oh, my gosh, I could use the chain rule 500 times here. This is going to be won over square. No, no, no, no, no, no. Don't do that. Uh huh. Okay, So why do I say don't do that? Well, if I take the derivative of this function with respect to X first we're going to get an absolute mess. And I would never want anybody to do that. Not even my worst enemy. But what would happen if I take the derivative with respect, Toe? Why? First, we'll notice what happens. This crazy complicated function over here does not depend on why Onley depends on X, So this is a constant. So the derivative with respect to why is just X? Because I take the derivative here. X is a constant derivative. Constant times y is X plus zero. Then I could take the derivative with respect to X, and I get one. Now, wait a minute. This is not answering the question that was asked for it says compute f ex wives to take the derivative with respect to X and then take the derivative with respect to why. But here I've taken the derivative of a why methods The derivative of f with respect, why and then with respect to X. But these were the same. I told you that most of the time things were going to be the same as long as the partial derivatives are continuous. But I can just see that this is an outbreak function. So it is a continuous function in any of its derivatives are going to be continuous wherever they're defined. So therefore, this function here is going to be equal distributive of why Then the derivative with respect X is gonna equal what we're looking for, which is one in this case

Multivariable Optimization

Multiple Integrals

Vector Calculus

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02:06

08:04

02:32

02:59