Which of the following is the value of directional derivative of the function f(x,y,z)= xy+ yz+zx at the point P(2, 2, 2) in the direction of the vector ü = 3ỉ +6j- 2k ? (a) 4 44 (b) (c) 44 (d) 7 (e) 28

Q: Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 2, 1) in the direction…

A: Here we have to find the directional derivative for given f(x, y, z).

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: Consider the function Question 1 x f(x, y) = -y ln x + x lny + y a) Find the directional derivative…

A: Hints: The given function is f(x,y)=-ylnx+xlny+xy The direction vector of a is a⇀a. Therefore the…

Q: of f(x, y, tion of ve

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Q: Determine the directional derivative of f(x, y, z) = tan-1 221) where U = (-1,2,2) at P(0, 1, 1).…

A: The given function is fx,y,z=tan-1xy22z2-1. The direction vector is u=-1,2,2 and the point is…

Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: 6. (a) Find the directional derivative of w = x²y² at the point (1, -3) in the direc- 5T 5T tion of…

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (-5, −1, −1), b = (−2,…

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Q: f f(x, y, z) = xy: on of vectorî - %3D

A:

Q: c) 3.5-1 -2.5 cm) 3 X WRONG y-y₁= m(x-x₁) y- 1 = 2.5/3 ↓- y=1=0.83(x-3) 9:/= 0.83x-2.5 +1 y=0.83€…

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Q: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

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Q: Find the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction…

A: Here, f(x, y, z) is given we have to find directional derivative of f(x, y, z) at point (2, 1,2) in…

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: Find the directional derivative of the function f(x, y,z) =x-y+2z at the point P(1,2,3) in the…

A: Note:- Let a function f(x, y, z), then Direction Derivative of the function f at point P in…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…

Q: 2. [-/16.66 Points] DETAILS Find the directional derivative of the function at the given point in…

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Q: Find the directional derivative of f(x,y,z) = x² + xy + z² at point (1,0,1) in the direction of z -…

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Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional derivative gives the rate of change of a function at a specific…