In this problem this asked to find Think they get off the given function f and then evaluating it. Did you that point B vino deck degraded off f that this day left? Is it going to do? And six f by I am sick. The best impartial, innovative off effort respect to X, then partial derivative off F with respect to buy and then partially defective off f with respect. To say so. This is a will do and fixed these two X divided by one plus X squared plus by square plus zigs good as F is given Toby Natural Law off. But plus X squared plus y squared plus X squared, It's dead even is. First we find the daily with their off l. A. That this one divided by X squared plus y squared plus takes square and then by chain rule it will be my people. And by the directive off one plus x squared plus y squared plus X quit we just two weeks. So in this two weeks, divided by bike plus X squared plus y squared plays a squid. Similarly, if what is so why do I date by one plus x squared plus by square plus six quid, huh? I've said is Does that divided by one plus x Quick bliss by square, plus the square. Now we will right into it In the form off you need directors. I j get so this would be first we can take Komen, don't divided by one plus x squared plus y squared plus x square from all the three components. So it went before divided by one plus x scripless Why scriptures x squared and my deep light but x why they so that can be done s thanks. I bless by j bless Zak Gay. This is the required Grady. And now we have devalued this executable 0.1 bun minus one. Then this We have to find the left egg but but minus one So it will be going do so divided by but plus X squared will also be one by square will also be one. And so expect that this minus one square will also be one. So denominator will be by plus one plus one plus one that this four my d blind by excited that this one I'm so I plus Bun J that this Jay less, minus one into OK, that this mine escape. So this is a going do one divided by do I bless day mine escape. Now the next question asked is to find the unit vector in the direction off Maximum increase off f and the give a point b vino there the direction off Maximum increase off F is in the direction off the great being off f that this day left Then this. We have to find the unit vector off then F unit Director off the left can be found us They left divided by magnitude Off they left We will first find the magnitude off they left be Just think will do another would be coefficients off i j k with this quest that this quest off the coefficient off I'm JK so coefficient of ice one by do and it's square is one by phone less coefficient off. J is one by two and saw its square is one by foot. Bless coefficient off case my nessman by do And so it's squared is bun by four. So this is a well do another route three by four are it Does it will do Route three divided by two. So the unit vector off the left will be going toe. The left is but if I did, I do I plus J minus k divided but magnitude. Off the left is rubes three divided by two. So this is it will do one divided by three as this tool. And this Toobin began. So so. One divided by 123 My team blind by I plus J minus cape. So the unit vector in the direction off maximum increase off F and B is one divided by fruit tea. I best day minus K. Now the next question asked is 25 later. Change off the function in the direction off Maximum Ingres egg be They have changed off the function in the direction off maximum in Greece is the magnitude off the great get off F that this magnitude off Della which we have found Toby quite withdrew. Three. Divided by Duke that this the rate of change of the function in the direction off maximum in please is Group three divided by two. Now the next question asked is to find the directional daily with direct T in the direction of the G one factor you'll by three Dubai three minus one by three This is think e one back toe like this big will do you first. We will check where there is a unique vector or not. Yes, it is a unique vector. So the directional daddy Wait too. In the direction off that you and give my 0.11 minus one. Is it quite do? By formula physique will do the great get off f at the same point that this 11 minus one dot product of it did You need vector in which we have to find the directional derivative like this you had. So this isn't will do Della at 11 minus one b have found is this one. So this is a quarto one divided by two. What coefficient off ice. One coefficient of jay's also and coefficient off case minus one. So if this but divided by two into one that is one divided by dough again one divided by do and then one divided by doing do minus one. That this minus one divided by two dark product bit. You had that. This our unit director, You bitches so divided by three so divided by three and minus one, divided by three. Now this is a quite do but divided by to my people. I two, divided by three, is so divided by six yes, but divided by two months. People have a two. Divided by three is, I think so. Divided by six less minus one, divided by two into minus one. Divided by 30 is one divided by six. So this is a goingto five, divided by six. That this the required directional daily rate is five divided by six, which is our required answer.