Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at the point (4,1). Give your answer as a unit vector.

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Rx, Y,…

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Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

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

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

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

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y): 4x sin(xy)…

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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)…

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Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

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

Q: Find the derivative of the vector function r(t)=ta×(b+tc) where a=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and…

A: Solved below

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: The function is given as f(x,y)=5xy . The point is x=2 and y=8 inclined at angle θ=π3. The…

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: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

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Q: Find the directional derivative of the function f(x,y, z) = V22+ y² + z² at point (2, -3, 6) in the…

A: In this question, we want to find the directional derivative of the given function at given point…

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

A: To find the maximum rate of change for the function f(x,y)=5xsin(xy) at point (2,3)

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

A: To find the Direction in which the maximum rate of change occurs for f(x,y)=3xsin(xy) at point (1,3)…

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…

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

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Q: 2. Find the directional derivative of the function f(x,y,z) = xy? – 4x?y + z² at (1, -1, 2) in the…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

A: According to the given information, it is required to find the directional derivative.

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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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Q: Represent the plane curve by a vector-valued function. 2x − 3y + 5 = 0

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Q: Let f(x, y, 2) = cos(ryz) Find the directional derivative of f at the point (,, 7) in the (a)…

A: We have to find Directional Derivative and Largest possible value.

Q: Find the direction in which the maximum rate of change occurs for the functio f(r, y) = 2x sin(ry)…

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Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

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Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

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A: Topic-vector calculas

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: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

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…

Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

Q: If f (x, y, z) = xy + xz + yz, find this function's directional derivative at (-1,3,5) in the…

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

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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…

A: We have to find the direction in which the maximum rate of change occurs for the function…

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

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Q: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

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