Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the direction of the unit vector U parallel to (-1,4, 2). %3D

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: 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: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

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Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(3,-√2,3). Calculate the directional derivative…

A: Here we will evaluate each expression.

Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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

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Q: the position vector r describes the path of  an object moving in space. (a) Find the velocity…

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Q: For the function f(x, y) (5,-4) that has a positive Question Help: D Video -4-2²-² 1 component. find…

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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: 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: The directional derivative of xy f(x, y) = x + y) at (1, 1) in the direction of the unit vector at…

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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…