f (x, y) = x² In(1+x² + y²)

Q: Find the gradient of the function at the given point. g(x, y) = 12xev/x, (6, 0) Vg(6, 0) =

A: Formula Gradient of function f(x,y) ∇f(x,y) = fx(x,y)i + fy(x,y)j Where  fx is partial derivative…

Q: Calculate the gradient. f (x, y) = cos(x^2 + y)

A: Calculate the gradient. f (x, y) = cos(x^2 + y).

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

A:

Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (18, 0) vg(18, 0) =

A:

Q: (a) z = x² + y² – 4x in P(1,2) (b) z = yln(x +y) in P(-3,4) %3D

A: a) Compute the gradient of z=x2+y2-4x in P1,2 as follows: It is known that the gradient is…

Q: Calculate the gradient. f(x, y) = cos(x³ + y) Vf =

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Q: Calculate the gradient Vf, where f (x, y) = In(x² + y²).

A: Given:- f(x,y)=lnx2+y2 To find:- Gradient of f ∇f

Q: Calculate the gradient of f(x, y) = sin(x² - y) Vf=

A: Finding the partial derivative of the function.

Q: Find the gradient of the function at the given point f(x, y) = 5x + 4y² + 1, (1,4) Vf(1, 4) =

A: Solution of given question is written in below steps.

Q: A. Find the gradient of the function. f(x,y. z) = 3x y + cos(32)

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

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 +6, (3, 1) Vf(3, 1) = 2i+…

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Q: Find the gradient of the function at the given point. f(x, y) = 3x + 5y2 + 8, (2, 1) Vf(2, 1) =

A: We have given function  fx,y=3x+5y2+8 fx=∂fx,y∂x fx=3∂x∂x+5∂y2∂x+∂8∂x fx=3+0+0 fx=3  .........(i)…

Q: Find the gradient of the function at the given point. g(x, y) = 18xe/x, (3, 0) Vg(3, 0) =

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Q: Find the gradient of the function at the given point g(x, y) = 2xe/x, (16, 0) Vg(16, 0) =

A:

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: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

A:

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 8,    (2, 1) ∇f(2, 1) =

A: We have to find the gradient of the function  f(x, y) = 2x+4y2+8  at the point (2, 1).

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

A: f(x,y)=5x+3y2+5 fx(x,y,z)=5fy(x,y,z)=3(2y)=6y∇f =fx(x,y,z) i +fy(x,y,z) j

Q: Find the gradient of the function f(r, h) = 2xrh + xr² at the point (2, 2). V f(2, 2) =

A: Given,   f(r,h)=2πrh+πr2

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 1, (1, 3) %3D Vf(1, 3) =

A: ∇f = <∂f/dx, df/dy> ∂f/dx = 4 df/dy = 10 y

Q: find the gradients of the functions below a)f (x, y, 2) = ye* + 22 in P(0, 2, :

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Q: Find the gradient of the function f(x, y) = x²y+y³. Vf(x, y) = xî+ (x + 3y²) ĵ ○ ▼ f(x, y) = xyî +…

A:

Q: Find the gradient of the function: f(x, y, z) = x'y + = OF = (7x + 6x°)i + 3y²j + k %3D OF = 7x°y°i…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 4, (3, 2) %3D Vf(3, 2) =

A: We will solve the problem.

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

A:

Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) = %3D

A: To find the gradient of the function at the given point.fx, y=5x+2y2+4, 4, 2∇f4, 2=?

Q: Compute the gradient Vf of the function f given by f(x, y) + y at an arbitrary point (x, y). Then…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

A:

Q: Find the gradient of the function at the given point. w = x tan(y + z), (17, 6, -3)

A:

Q: Find the gradient of the function at the given point. g(x, y) = 5xev/x, (8, 0)

A: Follow the procedure given below.

Q: Compute the gradient of each of the following functions. а. f(х, у, 2) %3D х sin(yz) b. f(x, y, z) =…

A:

Q: Find the gradient of the function f(x, y) = 3x + 5y2 + 1, at the given point      (2, 1)

A: Given equation - f(x,y) = 3x+5y2+1We can write it as - y = 3x+5y2+1Gradient is given by , dydxNow…

Q: Find the gradient Vf at the given point, and compute the directional derivative of the function in…

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Q: Find the gradient field for the function f(x, y) = x2+y2

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Q: Compute the gradient of the function at the given point. f(x, y) = 5x2 + 10y, (4,-3) Vf = 80i - 30j…

A: As per the instruction, we will answer the first one. Given: Now,         ∇f=fxi+fyj     =10xi+10j…

Q: Calculate the gradient of h(x, y, z) = x2 Z

A: Given h(x,y,z)=x1y3z. The objective is to find the gradient of h.

Q: Find the gradient of the function w = x tan( y + z), at the given point (4, 3, −1)

A:

Q: Find the gradient of the function at the given point. In(x² – y) – 3, (3, 8) z = 1 Vz(3, 8) = 2i

A: I have checked the work. Calculation is correct.

Q: (е) f (х, у) %3D V2х + Зу in P(-1,2) in P(4,–2) (f) z = -1 tan y

A: We are given : f(x,y)=2x+3y in P(-1,2) Now,…

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

A:

Q: _f (x, y) = ryey

A: We can find the gradient as below.

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

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

A:

Q: Find the gradient of the function at the given point. g(x, y) = 20xeY/x, (9, 0) %3D Vg(9, 0) =

A: We can find the gradient as below.

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

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

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y² + 4, (1, 2) Vf(1, 2) =

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

A: