Find the gradient of f(x,y.z)= (x2 + y2 + z2) - 1/2 + In (xyz) at the point (1,- 2, - 2) %3D Vf (1. -2, - 2) = (D+ (Di+ (OK (Type integers or simplified fractions.)

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: Given the function below f(x, y, z) = 2 cos (r) + xy - xz - y² - e²% +2% (a) Show that the origin…

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

Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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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 F(x,y,z)= (xy^2)lnz

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vf|(−2,2,− 1) = ₁ + Oj + k (Type integers or…

A: We want to find the gradient of the given function at point (-2,2,-1).

Q: Use the Chain Rule to evaluate the partial derivative at the point (u, v) = (0,5), where g(x, y) = x…

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Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

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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: Use the Chain Rule to evaluate the partial derivative at the point specified. ∂f/∂s at (r, s) = (1,…

A: Use the Chain Rule to evaluate the partial derivative at the point specified. ∂f/∂s at (r, s) = (1,…

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: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: Compute the partial derivative of the function f(r, y, z) = e'-z cos(y) + z e=1/(1+y²) vith respect…

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Q: Compute the partial derivative of the function * f(x, y, z)= el-roos(y) +2e=1/(1+²)

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Q: Find the partial derivative of f(x, y) 8x - 2xy2 + y3 with respect to x at the point (2, 1, 61).

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Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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

A:

Q: Find the gradient of the function at the given point. In(x² – y) – 8, (3, 8) Vz(3, 8) =

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Q: Find the gradient of the function f(r, y, 2) = x In(yz), at the point (-2, 1, e) Vf(-2, 1, e) =

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Q: Calculate the gradient of h(x, y, z) = ÷ 1, Vh <-1/(x^2y)z,-1/(xy^2)z, 1/(xy):

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Q: Find the gradient of the function f(x,y,z)=y^(2)ln(xz), at the point (1,−1,e) ∇f(1,−1,e)=?

A: Given query is to find the gradient of f(x,y,z) at a point (1,-1,e).

Q: f(x, Y, z) =

A: We are asked to find the gradient of the function.

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 the function at the given point. In(x² – y) – 6, (3, 8) z = Vz(3, 8) =

A:

Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

A:

Q: Find the gradient of f(x, y) =x2-5xy+y2 at the point (0, 1)

A: Gradient of the f(x,y) at a point (a,b) is given by :∇f=dfdx(a,b)i+dfdy(a,b)j

Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

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

A:

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

A:

Q: Find the gradient of the function f(x,y,z)=2xe^(y/3)sin(3z). grad f=

A: Given f(x,y,z)=2xe(y/3)sin(3z) We need to find gradient of f(x,y,z)

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

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Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: Find the gradient of f(x,y,z)=xy+yz+xz at point P(1,2,3).

A: As we know that the expression for the gradient is: ∇fx,y,z=i∂∂x+j∂∂y+k∂∂zfx,y,z Given:…

Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

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Q: Find the gradient of the function f(x,y, z) = xy°z³ at the point (1,1,1).

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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 at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = Z

A: for finding gradient we have to find the derivative with respect to x and y   z  = ln(x2 -y)/x - 3…

Q: Find the gradient of the function In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

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Q: find the work done by the gradient of f(x,y,z) =ze^x+2y^2z along the path from (1,2,4) to (-1,0,5)

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Q: The gradient of f(x, y) = ry at (x, y) = (3, 1) is %3D

A: Explanation and solutions is given below....

Q: Find the gradient of f(x,y,z) = sin x ln y + z^3

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

A: Given functions are

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

A: