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Use the gradient to find the directional derivative of the function at P in the direction of PQ_g(x, Y, 2) = xyeP(2, 6, 0), Q(O, 0, 0)Need Help?Read ItWhtchItiSubmi...

Question

Use the gradient to find the directional derivative of the function at P in the direction of PQ_g(x, Y, 2) = xyeP(2, 6, 0), Q(O, 0, 0)Need Help?Read ItWhtchItiSubmit Answer

Use the gradient to find the directional derivative of the function at P in the direction of PQ_ g(x, Y, 2) = xye P(2, 6, 0), Q(O, 0, 0) Need Help? Read It WhtchIti Submit Answer



Answers

Use the gradient to find the directional derivative of the function at $P$ in the direction of $Q$ $$g(x, y)=x^{2}+y^{2}+1, \quad P(1,2), \quad Q(2,3)$$

For the given question we need to find a dia solidarity of this function at the point in the direction of you. First to find a gradient affair which is the leopard lX icap plus the left bundle way Jacob, not a leopard elections different shooting this function with respect to X. That will be 66 icap plus the leopard elements differently in this function with respect to Y. So we have minus two Y. J. Cap. At a given point. At the end of a further point we will be quarter six times minus one Icap minus two times for the cap. So that will be minus six icac minus eight Jacob. Now we need to find out vector in this direction. So vector we will be quarto three minus minus four I cup plus six minus four year cap. That is equal to four. I kept to jacket. Now the unit vector in the direction will be a quarter four. I kept to jack up If I had a square or tough four square plus two square that is called to one by rotor of 24. Icap left to Jacob now went to find a dash and derivative F, which would be the advent of effort, the point p dot opportunity, but it will be until the minus six cycle minus L. Jacker. Not productive. And my editor of 20 for I got to say That is according to one quarter of 20-24 -16. Take her to -40. I wrote out of 20, which is called -4-5. I said, No final answer.

In the given question we need to find a dietitian and the beauty of this function at this point. And in the given direction. First to find out their 25th which is the left Alex I kept by Delroy Jacob. So that will go to I've got the legs of ex wife, Hi Cap plus delta Del way of X. Y. Yeah. Okay. That would be called to why I cap plus X. Check up at a given point at the end of F. At little minus two will be called to -2. My cap plus cap so that is -2 can. So the device and the motive in this direction will be called to the president of F. At the local miners. To that product with we that will be called to minus to hike up. Don't put up with one x 2. I got a lot of power through Jacob so that only one to minus two might have the one. They were going to The call to -1. Southern Iceland motive. Did you call to -1

Think of us The function he of excellent is equal to the natural long of four plus x squared plus y squared. And they're gonna want a computer directional derivative. So it's compete, ingredient or natural Law given input is one over that input times the derivative of that input. But we're impartial. Your suspect X We're actually gonna have to Exxon's up for the why. It'll be similar, but we'll have a to y on top when we do the chain rollers suspect blind. Okay, so now let's evaluate at the point they want us to take our ingredient. It's at the point. Negative one come on to Well, it's fine. Muncie on the bottom like that. I mean, it is the same. Every right. We'll end up with the four plus one plus for so dividing by nine on the top. We have a negative too. So they have to overnight with Chris. Component on the right will be four overnight. All right? And they're gonna want us to compute this directional derivative in the direction. Teoh, comma one. Well, we know the unit vector that corresponds to that will be. Do you over the square defined one over is very violent. So when we're going to compute the directional derivative and that you direction of P, or you need to compute the dot product of our little unit back there and are given ingredient at the point, so what we're gonna end up with is, let's see negative for over a nine square root of by plus for over nine scripture to five that just comes out zero. So the direction already about that boy is actually zero. That's pretty cool traveling along the level curves still at that point in that direction.

For the given question. We need to find the national director of dysfunction at the point B. And the direction of cube was to find the gradient of G. C D. L. G by telex I kept plus delegate by delegate. Cap pastel chief. But L. J. K cab. So Daljit metallics gives us why the power icap plus delta delta gives exit to the larger the cap plus X. Way to the party pick up. Are the given point. We have threatened to Mci. At that point he will be called to Putting except for two. Why it's called the four and that is called Syrup the 24. It took the power zero icap just to look the part zero Jacob less eight with the paris. Okay cap that is according to four icap stools a cap plus eight A cap. Now in this, in the direction we need to find the vector U. That will basically go miners to icap plus zero miners. Four cheer camp Placido zero K. Cab. That is all to minus two. Icap minus four. Thinker. The instructor will be, you divided the magnitude of you, little recalled to minus two, I ca minus four Jacker, divided by two route five. This can return, it's minus I ca minus two seconds. You had a good fight so and Iceland energy will be. Do you see will be the identical scene at that point we not put up with you can Italy for icap plus Tuesday cap. Let's kick it dot perfect and a cycle understood jacket 235 Until a quarter to -4 -40 buttons for about five. So the correct answer it -8945.


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