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Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Boston College

0:00

Jsdfio K.

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

00:59

Andy S.

Kim H.

00:33

Dungarsinh P.

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So you look at this question, You say Wait a second. This is just a couch. One question and you're exactly right. But now remember, we have some justification for implicit differentiation, and we also have a really slick way to do it. So what I'm gonna do is I'm going to say ffx. Why is X squared y plus why Squared X plus Tan X Y yeah. Now, why did I do that? Because if you recall what we said about implicit differentiation, do I. D. X is just minus the partial derivative of this with respect to X divided the partial divided by the partial derivative of this function with respect to why. But this is a walk in the park. The partial derivative of this, with respect to X, is going to be two x y plus. Why squared? Plus, we're going to get a Sikh and squared, and then we differentiate with respect. Toe exit will get a factor. Why and then all over the partial. With respect to why which is just X squared plus two x y plus, This time we'll take the partial of the inside with respect to why, so we'll get X and then seeking squared next. Why? And we're done. And now if you don't believe me, that this is refreshing. Well, for negative. Yes. If you don't believe me, that this is a really refreshing way to do this. Try to take the derivative here, find why, prime Just using implicit differentiation as you did in cop corn. And what you're going to see is that you're gonna have a bunch of D y DX is that you're gonna have to kind of combined together. You're gonna have toe do some algebra, subject things over. This is a lot slicker using the techniques using these partial derivatives.

Multivariable Optimization

Multiple Integrals

Vector Calculus

02:59