5

Suppose that f is differentiable function with fx(0,0) = 5 and f,(0,0) = 4. Let wlu;v) =f(x(u,v). Yu,v)) whcre cOs u + 4 sin and y = cos Sin v.Find Wu(7/2,0) .SavcS...

Question

Suppose that f is differentiable function with fx(0,0) = 5 and f,(0,0) = 4. Let wlu;v) =f(x(u,v). Yu,v)) whcre cOs u + 4 sin and y = cos Sin v.Find Wu(7/2,0) .SavcSubmit Problem #3 for GradingProblem #3 Attempr #1 Your Answer: Your Mark: 0/2*Attempr #2Attempt /2

Suppose that f is differentiable function with fx(0,0) = 5 and f,(0,0) = 4. Let wlu;v) =f(x(u,v). Yu,v)) whcre cOs u + 4 sin and y = cos Sin v. Find Wu(7/2,0) . Savc Submit Problem #3 for Grading Problem #3 Attempr #1 Your Answer: Your Mark: 0/2* Attempr #2 Attempt /2



Answers

In Problems $35-40, f$ and $g$ are differentiable functions. Find $F^{\prime}(1)$ if $f(1)=2, f^{\prime}(1)=-3,$ and $g(1)=6, g^{\prime}(1)=2$. $$ F(x)=\left(\frac{4}{x}+f(x)\right) g(x) $$

Right. The way that you should approach this problem is to just treat the two that's in front. Yes, it's multiplied, but it's just a constant as well. That's a lowercase F times G FX. So as far as I'm concerned, the only product I need to concern myself is this one um to do the product rule. So then the derivative. Uh that too is just going to go along for the ride where you do two times the first function is left alone times the derivative of the second function, and then plus The two is still there. But now it's the derivative of F. And you leave G alone. So when it's time to figure out F prime of one, which is what they ask you for, uh those twos are still part of the problem and you could factor it out if you wanted to, But f of one equals 2. Uh F prime of one equals negative three. So there's times in there G. of one equal 6, and G prime of one equals two, So two times two times two and give me eight, two times 3 is six, uh times another six is 36. And notice the negative there, And 8 -36 would give me -28. And as long as my math is correct, that should be a perfect answer.

There's a lot going on in this problem. So I'm gonna just jump right into it Where you have 1000, lower case F. A bex. And then the denominator you have x minus G. Fx. Just double checking that I copy that down correctly. Because what they ask for is not just F prime of X, but they asked for F prime of one, I'm going to start with finding F prime of X, which would be the derivative of the top, which is just to f prime of X. Times you leave the denominator alone and a minus now you leave the top alone. That's that one plus two alfa Becks uh times you leave the denominator alone, which is uh one minus G prime of X. So you take the derivative of the bottom all over the denominator, which is that X minus G of X squared. So now when you're asked to evaluate what F prime of one is, you need to plug in one in for all those, you're talking about two f prime of one times the quantity of one minus G of one minus the quantity of one plus two F of one Times one -G. Prime of one All over again. XS one -G upon and whatever that number is squared. So as you go back to the directions you start filling in That f prime of one is -3. So you have to negative three. Let's see. And then G of one is to find a six. And we also have them the denominator on hopes. No, I'm not too sure. 196 Squared. I don't think I have any other G F ones in here. Uh f of one is defined as two And then G prime of one is defined as two. So as we go to evaluate all this, let's see. We have two times 93 is 96 times 95. We give me 30, Let's say 1-plus 4 would give me five times negative one And 1 -6 is -5 square. To give me positive 25. So we're looking at 35 25th. So If you divide both top and bottom by five, he gets seven fists. Mhm.

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.

There are several ways of approaching this problem because there are two products, there's a product after the X squared and there's also a product after F of X. So what I would actually do is just put like a brackets here. So when I go to define the product, I would leave the X squared alone and then I would take the derivative of F of X times G of X, which is a product rule. Yeah. Leave alone. Take the derivative plus take the derivative. Leave alone. So, but you're still not done because then you have to finish the product rule with X squared times what was bracketed and red. Where you take the derivative of X squared, which is two X. And you leave Effa Becks and G Fx alone. Well now we're ready to figure out what F prime of one is. What I like about this is one squared is just one, Overhears two Times 1. And then you can go back and see, okay, well, F F one is to find us too, you know, so we have a two here. We also have a two here. Let's see. G. of X is defined G of one is to find us six. So I have a six year And we have a six here and then C F prime is defined as negative three at X equals one, and G. Prime is defined as two at X equals one. So just to simplify that, just make sure that you do the proper order, you know, four plus negative 18 when you multiply correctly there and two times 2 before um Times six. Give Me 24. So we're looking at negative 14 plus 24 In the proper order to give us a positive 10 for F. Prime A one.


Similar Solved Questions

5 answers
1) Consider the reactionproducts From the following data obtained at & certain [emperature, calculate the rate constant; determine the Order 0f the reackon 2713o0droWto
1) Consider the reaction products From the following data obtained at & certain [emperature, calculate the rate constant; determine the Order 0f the reackon 271 3o0dro Wto...
5 answers
POCIHCNbaseCH,MgBrCro;H;o"ether , H;o"(CF_COzhHgOH2 CH;CHZCH_OH NaBHaDIBAL; tolueneChyohHjo"
POCI HCN base CH,MgBr Cro; H;o" ether , H;o" (CF_COzhHg OH 2 CH;CHZCH_OH NaBHa DIBAL; toluene Chyoh Hjo"...
5 answers
8218319 Chhich is ? protein structure on the centromere that Is the chromatids? point of aitachment between the miotic sohdlatnd eietMultiple ChoiceCentrosomeKinetochoreMetophaen pInteSpliceosome
821831 9 Chhich is ? protein structure on the centromere that Is the chromatids? point of aitachment between the miotic sohdlatnd eiet Multiple Choice Centrosome Kinetochore Metophaen pInte Spliceosome...
5 answers
Jalli3331Iuin Uacuuin ravett nght with wavekngtn J80 (VA %8 the light In water? (5 pointa) mavelengthIls firsttor wtlch 610 . nm Orangt botween two sIlte (2) Whst Is Ihc scpuration Jklc 0/ 30.0"felling On single for 550 rin Iight ix thc frst mirimum (dark fringe) (3) At whnt Jnkk of width 100 mum?
Jalli 3331 Iuin Uacuuin ravett nght with wavekngtn J80 (VA %8 the light In water? (5 pointa) mavelength Ils first tor wtlch 610 . nm Orangt botween two sIlte (2) Whst Is Ihc scpuration Jklc 0/ 30.0" felling On single for 550 rin Iight ix thc frst mirimum (dark fringe) (3) At whnt Jnkk of width ...
5 answers
8 i VL N 8 1 1 8 7 1 } 58 Ze Fpl 0 1 [ 1 #e 1 1 l 2 [ H 2 } 1 } L } 8 1 1 2 Hi H 0 I V 1 1 j }1 1
8 i VL N 8 1 1 8 7 1 } 58 Ze Fpl 0 1 [ 1 #e 1 1 l 2 [ H 2 } 1 } L } 8 1 1 2 Hi H 0 I V 1 1 j } 1 1...
5 answers
Read the given paragraph. In the resting state, the axonal membrane is (i) with more (ii) charged ions outside than inside. This unequal distribution of ions is due to (1) the selective permeability of the membrane, which forms an almost impenetrable barrier to _iii) and (2) the action of the (iv) which pumps (v) $mathrm{Na}^{+}$out of the neuron for every (vi) $K^{+}$brought in. Select the option that correctly fills the blanks in the paragraph.
Read the given paragraph. In the resting state, the axonal membrane is (i) with more (ii) charged ions outside than inside. This unequal distribution of ions is due to (1) the selective permeability of the membrane, which forms an almost impenetrable barrier to _iii) and (2) the action of the (iv) w...
5 answers
Erm 1833 2 2 = €3 7 < 5+7) 2n
erm 183 3 2 2 = € 3 7 < 5+7) 2n...
5 answers
Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in part (a) by using the table feature of the graphing utility. $$g(x)=3 x^{4}+4 x^{3}-3$$
Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in pa...
1 answers
Compare the rates of growth of the functions $f(x)=\ln x$ and $g(x)=\sqrt{x}$ by drawing their graphs on a common screen using the viewing rectangle $[-1,30]$ by $[-1,6]$.
Compare the rates of growth of the functions $f(x)=\ln x$ and $g(x)=\sqrt{x}$ by drawing their graphs on a common screen using the viewing rectangle $[-1,30]$ by $[-1,6]$....
1 answers
Use a vertical format to find each product. $$\begin{aligned}&3 y^{3}+2 y^{2}+y+4\\&y+3\end{aligned}$$
Use a vertical format to find each product. $$\begin{aligned}&3 y^{3}+2 y^{2}+y+4\\&y+3\end{aligned}$$...
5 answers
An 75.0 kg spacewalking astronaut pushes off a 660 kg satellite,exerting a 85.0 N force for the 0.430 s it takes him to straightenhis arms. Part A How far apart are the astronaut and the satelliteafter 1.10 min? Express your answer with the appropriate units.All I want to know is how to draw a free body diagram forthis. How would I draw one?
An 75.0 kg spacewalking astronaut pushes off a 660 kg satellite, exerting a 85.0 N force for the 0.430 s it takes him to straighten his arms. Part A How far apart are the astronaut and the satellite after 1.10 min? Express your answer with the appropriate units. All I want to know is how to draw a f...
5 answers
Eproduco de la siguiente reacion [1]MgBr 2 equiv: [2] HzoOCHzSeleccione una:
Eproduco de la siguiente reacion [1] MgBr 2 equiv: [2] Hzo OCHz Seleccione una:...
5 answers
How much energy is required to melt 249 g of ice into liquid water at 0 'C? The heat of fusion for water is 333.6 Jlgenergy required:
How much energy is required to melt 249 g of ice into liquid water at 0 'C? The heat of fusion for water is 333.6 Jlg energy required:...
5 answers
Problem 3: Draw trans-1-ethyl-3-methylcyclohexane in all possible chair conformations_ Clearly indicate which of your drawings is the most stable and clearly explain why in less than 15 words (5 points)
Problem 3: Draw trans-1-ethyl-3-methylcyclohexane in all possible chair conformations_ Clearly indicate which of your drawings is the most stable and clearly explain why in less than 15 words (5 points)...
5 answers
32. Show that if n is a positive integer; then (2n 2 =262) +n?b) by algebraic manipulation.
32. Show that if n is a positive integer; then (2n 2 =262) +n? b) by algebraic manipulation....
5 answers
0 & R 1 M 66iiinuadri
0 & R 1 M 6 6iiinuadri...
5 answers
8.3.109Queston HulpAvmlak I5 0 Iurlni " J00 &w sunLud deviation = Dtemng Ihe qusutved Yiua d tne Mandentucnytole 4iei M (Roudl Lo Uhee docim ] pikes thd ) 4uetSuxtari observatione Ihg varabla have Atlesun 116 and swnple stardurd demtionstuxtenlizad versjon 0 ;CmdL1lchiclElehueCnc2
8.3.109 Queston Hulp Avmlak I5 0 Iurlni " J00 &w sunLud deviation = Dtemng Ihe qusutved Yiua d tne Mandentucnytole 4iei M (Roudl Lo Uhee docim ] pikes thd ) 4uet Suxtari observatione Ihg varabla have Atlesun 116 and swnple stardurd demtion stuxtenlizad versjon 0 ; Cmd L1l chicl Ele hue Cnc ...
5 answers
Light rays that are near and parallel to the principal axis of a concave mirror converge to a point 22 cm in front of the mirror. What is the radius of curvature of the mirror?Select one: a. -11 cmb. 36cm c.44 cm d.-36 cm
Light rays that are near and parallel to the principal axis of a concave mirror converge to a point 22 cm in front of the mirror. What is the radius of curvature of the mirror? Select one: a. -11 cm b. 36cm c.44 cm d.-36 cm...

-- 0.018975--