Find the a unit vector in the direction of which f(x, y) = In (1 + xy) increases the most rapidly at (2,3). What is the maximum rate of increase?

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Q: determine the unit vector of the direction from which f grows fastest in P and determine the rate of…

A: Here I am attaching image so that you understand each and every step.

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A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 1. Find the directional derivative of f(x,y) = In(a2 + y²) at the point P(2,1) in the direction of…

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Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

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A: Instantaneous rate of change of a function g in the direction of a vector v is  =∇g.vv Maximum rate…

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A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

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Q: Q1. Calculate the directional derivative of f (x, y, z) of vector v =i+2j+3k. = xyz at point P =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: nd the directional derivative of the function f(z, Y) In(z +y) at the point (3, – 1) in the rection…

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Q: Again just working on examples for exam, would like to see how you solve this to see if it is the…

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Q: Find the directional derivative of the function f(r, y) = 1+5x /j at the point (5, 1) %3D in the…

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Q: Find the directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

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A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

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A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

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Q: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

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Q: 3. Find the directional derivative of f(x, y, z) =x*y-yz' +z at the point (1, -2,0) in the direction…

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Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Find the maximum rate of change of f(x, y) Maximum rate of change: = In(x² + y?) at the point (3, 1)…

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Q: a) What is the rate of change of f(x, y) = 3xy + y^2  at the point (2, 4) in the direction of vector…

A: (a) Given Data: Function: f(x, y)=3xy+y2 Point: (x, y)=(2, 4) Direction of vector: v=-3i-j The…

Q: (b) Identify the unit vector ū pointing in the direction of maximum increase of the function f(x, y)…

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Q: Find the directional derivative of f(x,y, z) = yz +x? at the point (3, 2,1) in the direction of a…

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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: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

Q: 2. Calculate the instantaneous rate of change of g at the point (4, 1,0) in the direction of the…

A: Please see the attachment

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A: Given the function f(x, y, z)=(x3-xy2-z).........(1) We have to find the derivative of the function…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

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Q: Find the directional derivative of the function f(x, y) = In(x + y²) at the point (1, - 1) in the…

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Q: Find the directional derivative of f(x,y,z) = x²z – xz³ + zy at the point (1, -2,0)in the direction…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

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Q: Let f(x, y) = x /G. At the point (1, 4), find a vector (a) In the direction of maximum rate of…

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Q: Find the directional derivative of the function f(x, y) = In(x + y?) at the point (– 1, – 2) in the…

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Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.