Find the gradient of the function: f(x, y, z) = x'y + = OF = (7x + 6x°)i + 3y²j + k %3D OF = 7x°y°i + 3x7y²j - 5x7 %3D OF= + 3x'y?j - 5x6 OF = (7x° + 6x°)i + 3y²j - k

Q: The gradient of f(x,y,z) = e*+Ysin z + (y + 1)arccOS x at point %3D will be given by DA (e-2, e, 0).…

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Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

Q: What is the gradient vector of a differentiable function ƒ(x, y)? How is it related to the…

A: The objective is to write what is the gradient vector of a differentiable function ƒ(x, y) and how…

Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Find the gradient of the function f(x, y, z) = yz², at the point (0, -1,–1) V f(0, –1, –1) =

A: fx, y, z=yz2 & the point is 0, -1, -1. Partially differentiating with respect to x, we get fxx,…

Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

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Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

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Q: Let f(x, y, z) = 3xz + sin(ry)e*. what is faz? Find the gradient at the point (0, 0, 0)?

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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: How is the linearization of f (x, y) at (a, b) defined?

A: given,          any function fx,y at a,b

Q: How do you compute the gradient of the functions ƒ(x, y) and ƒ(x, y, z)?

A: Given, The function f(x,y). It's gradient is given by, For example,

Q: .    Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to…

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Q: Please show your answer to at least 4 decimal places. Determine the gradient of f(x, y) = e" sin(4y)…

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Q: Find the directional derivative of the function f(x, y, z) = ryz in the direction normal to the…

A: We havefx,y,z=xyz

Q: Find the gradient of f(x,y.z)= (x2 + y2 + z2) - 1/2 + In (xyz) at the point (1,- 2, - 2) %3D Vf (1.…

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Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

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Q: The gradient of f(x, y) = zy at (z, y) = ( – 2, – 1) is %3D

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Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: Find the gradient of the function w = xy2z2,  and the maximum value of the directional derivative at…

A: Given function:    w=xy2z2

Q: Find the gradient of the ellipse 2x2 + 3y2 = 14 at the points where x = 1

A: It is given that the equation of an ellipse is ;  2x2+3y2 = 14 We have to find the gradient of the…

Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

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Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: Use the Chain Rule to evaluate the partial derivative at the point specified. ag at (u, v) = (0, 1),…

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Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

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Q: Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to (-1, 0,…

A: The gradient of f(x, y, z) is:

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

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Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

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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,…

A: According to the given information, it is required to find the maximum rate of change of f at the…

Q: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

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Q: Find the directional derivative of the function at the point in the direction given. f (x, y, z) =…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Find the gradient of the functions below. a)f (x, y, z) = sin(xyz)

A: Here we will find out the required value.

Q: Find the gradient of the function at the given point. Function Point x + 2y y + 1 f(x, у) 3D (1, 2)…

A: Find the gradient of the function at the given point & find the maximum value of the directional…

Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: First, compute the gradient of the function p(x,y)= 12- 2x-y Then evaluate it at the point (- 1,2).

A: We need to find partial derivatives with respect to x and y to find gradient

Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

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Q: Find the gradient of the function f(x, y) = 7x2 + 6y, at the point (-2, 6). [ i.e., find V f(-2,6) ]

A: As we know that the expression of the gradient of the function is: ∇fx,y=i∂∂x+j∂∂yfx,y Given:…

Q: Find the gradient of the function at the given point. In(x2 - у) - 3, (2, э) Vz(2, 3) = %3D

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Q: Integrate f(x,y, z) = 2x – 3y² – 2z+3 over the line segment from the origin to (1, 1, 1) and over…

A: A parametric curve is a normal curve where we choose to define the curve`s x and y values in terms…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: Find the gradient of the function f(x, y) = (x + y)/(y + 1),and the maximum value of the directional…

A: Given: fx,y=x+yy+1 The gradient of fx,y can be calculated as, ∇fx,y=i^∂∂xfx,y+j^∂∂yfx,y Here,…

Q: Calculate the gradient of the function f(x, y) = cos (4z² – 4y) O a.-8z sin (4x2 4y)i + 4 sin (4x2 –…

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Q: Find the gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve

Q: Use the Chain Rule to calculate the partial derivative. Express the answer in terms of the…

A: Given functions are

Q: Please show your answer to at least 4 decimal places. Determine the gradient of f(r, y) = e sin(4y)…

A: The gradient is just the vector of partial derivatives.

Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

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