Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector making an angle of pi/6 with f(1,2,3). Fu=?

Q: Find the maximum rate of change of f(x, y, z) = x + y/z at the point (1, 1, -5) and the direction in…

A: We have to find the maximum rate of change

Q: You need to find the directional derivative of the functian f(x,y) = tan" (x4) at the point (2,2) in…

A: The given function is fx,y=tan-1xy. The main objective is to find the directional derivative of the…

Q: 4. Find the directional derivative of f in the direction of vector v at point (1,3) such that v =…

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

A: we have to find the directional derivative of f

Q: Please show your answers to at least 4 decimal places. Find the directional derivative of the…

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Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

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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: 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: 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: Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0F at  (12,12,12)…

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Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

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…

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

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

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in…

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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 f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

Q: Determine the directional derivative of f(x, Y, z) · = tan-1 ( where xy2 222-1 (-1,2, 2) at P(0, 1,…

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Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

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: What is the definition of the directional derivative for afunction of three variables, f (x, y, z)?…

A: The directional derivative of f(x,y,z) in the direction of the unit vector u=⟨a,b,c⟩ is given by,…

Q: Find the directional derivative of the function if f (x, y, z) = 3e* cos(yz) at point %3D (0, 0, 0)…

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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: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

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

Q: Find the normal vector to the tangent plane of z = 6e- Öy at the point (12, 24, 6). x component = y…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: an object is moving in 3-dimensional space with velocity vector v(t)=(sin(t),t,t^2) starting at…

A: Consider the given velocity vector: vt=sint,t,t2 Find the position vector: Integrate velocity vector…

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (3, 5) and the direction in…

A: Here is the solution of the given problem. Unit Direction:

Q: Find the directional derivative of f(x, y, z) point (1, 2, 3) in the direction of a vector making an…

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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 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: Find the two-unit vectors that are parallel to the tangent line to the curve y =x2sin(x) at the…

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Q: Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25…

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Q: If f(x,y) = ln(xy) + x^2y^2, how do I calculate the second directional derivative of f in the…

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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: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (5, 2) and the direction in…

A: As per bartleby guidelines, for more than one questions only 1st one is to be answered. Please…

Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (1, -4) and the direction in…

A: Here, the given function is: f(x,y)=ln(x2+y2)

Q: Find the directional derivative of the function: f(x, y) = ez² + 4y at the point (0, 0) in the…

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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

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 Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

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Q: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

A: Given: fx,y,z=4x-y2e3xz       at     2,-1,0 Directional Derivative = Gradient of function x unit…

Q: a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4),…

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Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (3, 5) and the direction in…

A: This is a problem related to the derivative of the function. For calculating the maximum rate of…

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

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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: nit vector that is parallel to the

A: Here have to find the unit vector that is parallel to the line tangent to the parabola y = x2 at the…

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

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