5

The directional derivative of H(T,y) at the point P = (4,5) in the direction of the unit vector &, Jz"+ Jzfis= 2, and the directional derivative of H(â‚...

Question

The directional derivative of H(T,y) at the point P = (4,5) in the direction of the unit vector &, Jz"+ Jzfis= 2, and the directional derivative of H(€,y) at the point P = (4,5) in the direction of the unit vector u2 V5* 4 35J is 3- Find the gradient VH(4,5) = H.+ HyJby solving for H_, and H, (4,5) in the following system of equations:H(4,5) .u, = 2 H(4,5) .uz = 3

The directional derivative of H(T,y) at the point P = (4,5) in the direction of the unit vector &, Jz"+ Jzfis= 2, and the directional derivative of H(€,y) at the point P = (4,5) in the direction of the unit vector u2 V5* 4 35J is 3- Find the gradient VH(4,5) = H.+ HyJby solving for H_, and H, (4,5) in the following system of equations: H(4,5) .u, = 2 H(4,5) .uz = 3



Answers

Computing directional derivatives with the gradient Compute the directional derivative of the following functions at the given point $P$ in the direction of the given vector. Be sure to use a unit vector for the direction vector. $$f(x, y)=3 x^{2}+2 y+5 ; P(1,2) ;\langle-3,4\rangle$$

Another in this problem, we were asked to find the directional derivative in the direction of the which is one comma one of this function F at the 0.34 Okay, so if we follow equation for from this chapter because he will need one over the length of the norm of this vector V and then we'll need the Grady int. So that'll be times the great end of F will evaluate that at the 0.34 And if the dot that radiant with the vector V, which is 11 Okay, so let's do what we can. First of all, length of the norm of 11 Uh, we just need to square those two and Adam together than take the square root. So one squared plus one squared is two squared of that will be of you scored of two. So that should be that first part for the Grady int. The definition is partial of F with respect to X partial of f with respect to why at the 0.34 and I don't doubt that as before, So we have won over this weird of two. Let's take these partial derivatives now the partial derivative of F with respect to X. That means why is a constant Well, the derivative of inverse tangent I remember is one over one plus right. Our input. There's X y squared now by the chain rule, you need to multiply that by the derivative of X y with respect to X. And that derivative is why so we ended multiplying everything by Why? Well, let's put that on top now The partial of f with respect to why you can see it's gonna be a completely symmetrical case. The same thing will happen. You get one over one plus x y all squared this time of the train rule applied to X y with respect to why the derivative his ex. So there is Argh! Radiant. And then we'll plug in 34 in a second. So we're getting there. So we have one of this word of two. Now let's just plug in three and four for X. So are three and four for X and Y. That means that the numerator here is four one plus well x times. Why three times for us 12 and 12 squared is 1 44 and then over here. Exes on top. So we get three over the same thing. The product with 11 That means you won over skirt escort of two times. So four over 1 45 three over 1 45 Product with 11 we get the ones sort of one on one over. Squared of two times. And that product. Luckily, one comma one is very easy to death product with you get for over 1 45 plus three over 1 45 Work was 37 Um, the numerator that denying there's the same So seven over 1 45 And then this is don't forget that scored of two. So you can simplify if you'd like, of course, But make sure your final answer is equivalent to this and you will be right.

Hi there in this problem, were asked to find the directional derivative of this function F in the direction of the vector four comma three at the point. One comment, too. So let's use the recipe and equation four for the directional derivative. So we will need one over the norm of, uh, this vector v you just for a common three over that length. Ah, then multiplied by the Grady into VF. That's the main thing here and specifically at the point. One comment, too. And then we'll need to take the dot product of that with their vector V two Guinness before common. Three. Okay, good. Ah, the norm of 43 We could use Pythagorean theorem, but hopefully these numbers are familiar. Right away we can see a little bit. Five. It's four square foot three scores 25 squared of that is five. So the length of the vector is five for the greedy INTs. Remember, we want the partial of effort, Respect, X partial of effort, respect toe. Why at the 0.12 That's just the definition of ingredient and this doesn't change, so they get 1/5 still partial of F with respect to X. We just look up here at F and we can see right away. That'll be two x The partial of F with respect. Why will be three wise squared? We'll plug in the point. Next. So at the 0.1 common too Put in one for X and two for why three times to square three times four is 12. Okay, we'll get 1/5 times have the dot product area. Two times four is 8 12 times three. I was 36. So 1/5 of get 44 they're so final answer for a directional derivative. 44 over five and we're done. Hopefully that

Okay, So for this question, the first thing we need to do is means to find the Grady in the f which is equal to why times eat the power off X times Why minus y square, comma ass minus two. Why multiplied by e to the power of X Y minus y squared. So once we have this, we can calculate the radiant at the point p, which is equal to two common native to whether the point p is too common to. So once we have this begin calculate the directional derivative off at the points to come too. Apply anything, hit the formula and simplifying to get 34 divided.

To compute the directional derivative of the given function. So that's compute its Grady. And first, let's scene okay at the point X wine. So we're going to get half goes up here, the Vector two x and negative Teoh for those partials, and we're going to want to plug in at the point. Negative one negative three. So let's see around it with a negative to here. And I am positive. Six year and they want the directional derivative in the direction. Three over file Negative for over five. Well, if you know your factory and triples, that's definitely a unit vector. So let's see the directional derivative. But seeing is going to be negative. 6/5, minus 24/5. So we end up with negative 30/5. But that's just negative. Six. Okay, clean


Similar Solved Questions

5 answers
Of the point On the curve Iy 8 in the first (20 points) (a) Use Calculus to find the coordinates quadrant that is closest to the point (0,0).
of the point On the curve Iy 8 in the first (20 points) (a) Use Calculus to find the coordinates quadrant that is closest to the point (0,0)....
5 answers
Treasurer), pts]: 8 ! chosen? organization with members, how many ways can committee composed of 3 people (President, VP , and
Treasurer), pts]: 8 ! chosen? organization with members, how many ways can committee composed of 3 people (President, VP , and...
5 answers
(15 points) Find parametric equations f(),9 = 9(),2 h(t) for the tangent line to the curve with x sin(2t) , y cO5 2 = at (0,_1,27) ,
(15 points) Find parametric equations f(),9 = 9(),2 h(t) for the tangent line to the curve with x sin(2t) , y cO5 2 = at (0,_1,27) ,...
5 answers
Constarspherically spreading EM wave comes from 800- source, Assume that the wave travels in free space.What is the intensity at distance of 4.2 Express your answer using two significant figuresAZdW/m?SubmitRequest AnswerPart BWhat is the rms value of the electric field at a distance of 4.2Express your answer to two significant figures and include the appropriate units:ValueUnitsErus
Constar spherically spreading EM wave comes from 800- source, Assume that the wave travels in free space. What is the intensity at distance of 4.2 Express your answer using two significant figures AZd W/m? Submit Request Answer Part B What is the rms value of the electric field at a distance of 4.2 ...
5 answers
Consider x2 _ 3y = 0. Find dr by implicit differentiation:Now, solve for y and take the derivative: Do you get the same answer both ways?
Consider x2 _ 3y = 0. Find dr by implicit differentiation: Now, solve for y and take the derivative: Do you get the same answer both ways?...
5 answers
E E & E SV O 46' nudnc (Select all that apply ) 4d 45 8 L HuAL C Vala= 1 1 EqualI0 musxt be Degative 1 L I (Wvol tonninon olMuchAl [LUIIL Ha(g) 2 1 1 1 1 11 Auicciedny LIc (cupcuul VuCM mhet 1
E E & E SV O 46' nudnc (Select all that apply ) 4d 45 8 L HuAL C Vala= 1 1 EqualI0 musxt be Degative 1 L I (Wvol tonninon olMuchAl [LUIIL Ha(g) 2 1 1 1 1 1 1 Auicciedny LIc (cupcuul VuCM mhet 1...
5 answers
Moving to anolher question will save Ihis response Question 5Quesuon 5 01 15667 pointsAnsterA police car emits sound with frequency 0l 1150 0 Hz 0at moving at 80 0 mls loxalds an obscrver inoving [ 20 0 m/s towards the police car The speed ol sound 340 MVs The Irequency heard by the ohsenvets in Ihe situalion iS 1742 1442 1652 1592 1532Clelun 6l 15question wiIll save Ihis response Moving t0 another
Moving to anolher question will save Ihis response Question 5 Quesuon 5 01 15 667 points Anster A police car emits sound with frequency 0l 1150 0 Hz 0at moving at 80 0 mls loxalds an obscrver inoving [ 20 0 m/s towards the police car The speed ol sound 340 MVs The Irequency heard by the ohsenvets ...
5 answers
Calculate the total area of the regions described. Do not count area beneath the $x$ -axis as negative. HINT [See Example 6.]Bounded by the $x$ -axis, the curve $y=x e^{x^{2}-1}$, and the lines $x=0$ and $x=1$
Calculate the total area of the regions described. Do not count area beneath the $x$ -axis as negative. HINT [See Example 6.] Bounded by the $x$ -axis, the curve $y=x e^{x^{2}-1}$, and the lines $x=0$ and $x=1$...
1 answers
In fatty-acid degradation, we encounter coenzyme A, mitochondrial matrix, trans double bonds, i-alcohols, $\beta$ -oxidation, $\mathrm{NAD}^{+}$ and $\mathrm{FAD},$ acetyl-CoA, and separate enzymes. What are the counterparts in fatty-acid synthesis?
In fatty-acid degradation, we encounter coenzyme A, mitochondrial matrix, trans double bonds, i-alcohols, $\beta$ -oxidation, $\mathrm{NAD}^{+}$ and $\mathrm{FAD},$ acetyl-CoA, and separate enzymes. What are the counterparts in fatty-acid synthesis?...
5 answers
IS your equilibrium: own example Blpainug using # H ditfrereierr principles_ initial temperatures_ but eventually
IS your equilibrium: own example Blpainug using # H ditfrereierr principles_ initial temperatures_ but eventually...
5 answers
0z NOILs3nOS+ 0 8-90 O4 0 5-*20 i Xquauuaja J0 Jaqunu uonlepixo a41 SI JEUM 94XH X paIle) Juauaja jeJuuaylodKy e BululeJuo) ajuensqns a41 Japisuoj61 NOIIS3OOE*p 0
0z NOILs3nO S+ 0 8-90 O4 0 5-*20 i Xquauuaja J0 Jaqunu uonlepixo a41 SI JEUM 94XH X paIle) Juauaja jeJuuaylodKy e BululeJuo) ajuensqns a41 Japisuoj 61 NOIIS3OO E*p 0...
1 answers
Evaluate each determinant by expanding by cofactors. $$\left|\begin{array}{rrrr} -1 & 3 & -2 & 5 \\ 2 & 1 & 0 & 1 \\ 1 & 3 & -2 & 5 \\ 2 & -1 & 0 & -1 \end{array}\right|$$
Evaluate each determinant by expanding by cofactors. $$\left|\begin{array}{rrrr} -1 & 3 & -2 & 5 \\ 2 & 1 & 0 & 1 \\ 1 & 3 & -2 & 5 \\ 2 & -1 & 0 & -1 \end{array}\right|$$...
5 answers
2. Sketch the line from Question 2 AND 3r + 2y = 12
2. Sketch the line from Question 2 AND 3r + 2y = 12...
5 answers
An economic instructor at UCF is interested in the earned in a course. Data collected relationship belween hours spent studying and lotal points students who took the course last semester follow #of observation(s) n = 19 #of independent variable(s) = 1 SSR 3,881 MSEFind the Value for the SST. Round to the closest integer
An economic instructor at UCF is interested in the earned in a course. Data collected relationship belween hours spent studying and lotal points students who took the course last semester follow #of observation(s) n = 19 #of independent variable(s) = 1 SSR 3,881 MSE Find the Value for the SST. Round...
5 answers
Match the correct graph $A-F$ to the function without using your calculator. Notice that there are more-functions than graphs; some of the functions are equivalent. After you have answered all of them, use a graphing calculator to check your answers. Each graph in this group is plotted on the window $[-2,2]$ by $[-4,4] .$$y=3^{x+1}$
Match the correct graph $A-F$ to the function without using your calculator. Notice that there are more-functions than graphs; some of the functions are equivalent. After you have answered all of them, use a graphing calculator to check your answers. Each graph in this group is plotted on the window...
5 answers
Alexis has a rectangular piece of paper of red paper that is 4 centimetres wide it's length is twice
Alexis has a rectangular piece of paper of red paper that is 4 centimetres wide it's length is twice...
4 answers
2. find the laplace inverse(s - 2)e` ~S F(s) = s2 _ 4s+3
2. find the laplace inverse (s - 2)e` ~S F(s) = s2 _ 4s+3...

-- 0.022363--