5

10. Let flx,y) =x exy a Compute allthe first and second partial derivatives of f fx(x,y) = exy(l+xy) fy(x,y) = xety fx(x,y) = ye"y(2+xy) fyy(x,y) = xety fy(x,y...

Question

10. Let flx,y) =x exy a Compute allthe first and second partial derivatives of f fx(x,y) = exy(l+xy) fy(x,y) = xety fx(x,y) = ye"y(2+xy) fyy(x,y) = xety fy(x,y) = xe "(2+xy) fyx(x,y) = xe"(2+xy)

10. Let flx,y) =x exy a Compute allthe first and second partial derivatives of f fx(x,y) = exy(l+xy) fy(x,y) = xety fx(x,y) = ye"y(2+xy) fyy(x,y) = xety fy(x,y) = xe "(2+xy) fyx(x,y) = xe"(2+xy)



Answers

In Exercises $3-10,$ use the Chain Rule to calculate the partial derivatives. Express the answer in terms of the independent variables.
$$
\frac{\partial f}{\partial u} ; f(x, y)=x^{2}+y^{2}, x=e^{u+v}, y=u+v
$$

Uh, yeah. Defined. Don't with over Don't way even that if you re equals you about blessed V on. Oh, this is Britain as keep buying about way we have u equals Esquire on a really good sex. So don't have over know why equals no over. No, you do know you know yes or no The be over why this is even as you know and stewed about you last be therefore No. When he was still ex unit our Squire, that's X because we're putting the Berries off even be so we'll be enough it or excuse about every squad plus excellent dancer to begin.

Thanks. Why you go do thanks, Devonian. But experts y square and the first thing mutual fight will be the partially rift. The other function respecting the X in this case here Extra bit variable on going a bit of constant. And here we noticed damage A Blinder Kocian room here therefore, by caution You again The extras. Why? For now the rift in an expert to one. So have the express by square. And that the review under Denominator consider plus two Thanks Busk y and then Thompson the X on the top it was going to find and we say we can cancel, uh, experts y and then we have experts quiet about three in the denominator on the time we have the express y does do banks and eventually gonna Three experts Why you running by X plus y out three And now the second thing we need to find a passion there. If there was fighting the why and here we used the cushion grew again and we still again the experts who I find the denominator on the camp we have Sorry isn't is a minus. Yeah, isn't minus isn't minus. So we get isn't to be the, uh Why minutes? Thanks. Here. Sorry about that. Why? Minus thanks. Yeah. And now in the second case, man, we have ah, minus thanks. Tamps Linda too. On Ben. Experts. Why? And then we can consider this exodus while with this power ahead and got about three different. I get a ministry to x over the, uh Thanks best Why I'm the three, and that is the answer.

This question asks us to use the changeable to calculate the partial derivatives and then expressed the answer in terms of the independent variables. Okay, we're looking at the partial derivative. First off. Okay, What we know we can do is we know that consults to axe is a squared. Therefore, why is to r us? Therefore, the partial derivative with F with respect to us is to terms to r us Times asked. Plus two times a squared times are this Simplifies to four r squared were just distributing now percent what you would do in algebra. These could be combined before and the two could be combined to give us six are asked squared. Okay, next value. We're doing the same thing here. We're drink partial derivative f with respect to our we're in the same substitution. Exes s squared Z is r squared this time we're just substituting. And why with Z Two times a squared times asked. Plus four times r squared times are we end up with two es cubed plus four r cubed. This is our second answer

Even the function year ICO to square root off the X one squared plus extra square plus actually the X and square and we can register as the x one squared plus x two squared plus start the top after the X and square power off Ah half and I want to find old armed up first personally reviewed the function immunised and we want to find ah ah specially written on a function with special and the X I hear So here means that X I will be the variable and then we will have no first manager by the power over here. So we bring the half down and then we have the X one squared That's x two squared up to the x end square. Then we have ah, well must have and terms by the general We need to apply in the rear of the under function inside for the X I So unless I would have excise somewhere here square So they removed of that one week Oh, Jew, the Jew X I hear. So if I'm wrong, we get echo. June, Uh, here we have the do you consider Would it Jewel and we have X I over the square root off x one square, but excuse could have arrested Don't come to the X and square. And for that I go to want you Actually, Er and I think we've been done the u over the X I.


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