Okay, so in this problem we are given that G is a function of you and be and we were told that is also a function can be written as a function where the X component is going to eat of the U plus sign a V. And eat of the U plus co sinuses. Right? Um So we'll give this table on the right hand side as well of functions of F G, F sub X and X and Y. And we are told to try to figure out um you know what the derivative of G would expect to you is and via is at zero comma zero. So what we do here is we're told that F is a function of X and Y and this is our function um um This is our function here. X. Right, this is our function X and this is our function. Why? So we can actually kind of write this as X. Of eucom avi and why have you come of it? And what's nice is we kind of know what X and y are. Right, this is the X coordinates. The functions of U and V. And y coordinates are the functions of you and be here and and so what's quite nice is that if we are trying to find G sub you, this is the same thing as trying to find f sub you of this kind of function here. Mhm. And this is again going to require us to use the chain rule now. This seems very very complicated up here but really it's just a simpler way of just saying, well, I have functioned that X is dependent on U and V. And moves with you and be the white queen, let's move with you. And be some kind of just making it a little bit more simple to have just the function now. And so in order to find the derivative with respect to you here, we again need to use the chamber as a reminder F now is a function of X and Y and X is a function of U. And V. And so is why. And so again, we can find that, you know, G cebu is going to just be equal to um the derivative of of of G with respect to you. Which is in this case the same thing as F here to have a F with respect to X. Multiply the river of X with this back to you. And again, we're using the derivative, the Dell signs because both of these X and F are functions of two variables. And similarly we get this exact same side. There are F with respect to Y and the derivative of Y with respect to you. And again, we can rewrite this very quickly and we note here and this is something I just want to know. This is the same thing as F sub X of X comma Y. Um and this is X. You know, w we know what the derivative X of you is right because X. We know what X Is right up here in the river of this function here. With respect to you. It's just you. The rule of F. With the spectacle Y. You can just write F sub Y. X. Comma Y. And this right here. Do you? Why do you the revenue of this with respect to you is just also eight of you. All simple. Now. What is F sub X. X comma Y. Well we're trying to find now This dysfunction at 0:00. Now this is really saying F sub X at X. But this is for you and V as a reminder but X is a function of U. And V as well. So the x. 00. And why at 00 times either. Do you times cheated Zero. Right? Sorry. Either the zero now because U. Is equal to zero plus F. Sub Y. And um At X. of 00. Why have 00 Times eight of the 0? First off of the zero is equal to one for both of these. I said 7 to 1 and the second one what is X. Of 00? Um Well We can plug in 00 To our function of X. Because this is our function X. Right here. So you fuckin 00. And this actually just gives us 80 plus sine of zero which is equal to one. This is F. Sub X. Of one. And we plug in 00 here. This would be one and this would be one as well. Co signer zero is one. So this would be to plus Fc wise this is again F. Sub Y. Of one common to. And all we get here is this means that F. Sub X. At one comma two. We look over here we go oh okay this is equal to just two. And we get that this is equal to five. And so this whole thing is equal to sell. Mhm. And that's how we get gsW at 00. We use the chain rule here. We remember that we can write the X coordinates in the white corns as functions of U. And V. And similarly we could do the same exact thing for Jason baby. And the only thing that would really change right, nothing else is really going to change that much overall. Um But we need to remember that um we would have this change here, this whole thing this part. Let me highlight this for you. What would change this part would change to a V. And this would also change to a V. Right? And so we would change that. That would be signed avi, we would have you know you would have a negative coast, you have coastline V. And then on this side you have so you would have co sign of the here and then this side you would have negative sign of the and then we get to go to the same exact process and you get a very similar answer. Um at this at this point you get a very similar answer because right, nothing else is going to change at all. We're still trying to find 00. So this part's gonna stay the same. This part's gonna stay the same. Just a matter of the coastline of v. As co sign of zero. And this is negative sine of zero, negative sine of 00. Co sign of zero is one. And so therefore you're going to get this answer as to yeah coming out there, something else changes. So as a reminder, make sure that you are just following the chain rule and understanding that that is just another way of writing the extra function of U. And V. And Y. Is a function of you.