Consider a function f(x, y) at the point (3, 1). At that point the function has directional derivatives: in the direction (parallel to) (4, 1), and 3 V17 in the direction (parallel to) (3, 2). The gradient of f at the point (3, 1) is 13 ).

Q: Use the gradient to find the directional derivative of the function w = 5x2 + 2xy − 3y2z at P (1, 0,…

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Q: What is the gradient of a function f(x, y) and why might we want to calculate it? How does it relate…

A: Properties of gradient of function

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: Use the gradient to find the directional derivative of the function at P in the direction PQ. f(x,…

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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: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

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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: Find the directional derivative of f(x, y) = x2y3 + xy2 in the direction ~v =< −3, 7 > at the…

A: f(x, y) = x2y3 + xy2 Please see the white board for the partial derivatives at the point (-1,…

Q: Find the gradient of the function f(x,y) = /4x+2y at the point (- 1,4). Then sketch the gradient…

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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 the following function fox, y) = (x – 2)^3 sin y, at (0,0]

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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. In(x² – y) – 6, (2, 3) z = Vz(2, 3) =

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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: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…

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

A: This is question of application of differentiation which we will proceed as follows

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

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Q: Find the directional derivatives of f(x,y,z) = x² y³ – y³z³ + x* in the direction of r = 2i– k, and…

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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: f(x, y) = e sin x, P(0,0), Q(2,1)

A: Consider the following function: fx,y=eysinx Gradient of the function:…

Q: =) Find the directional derivative at the point P = (2, 1, 1) of the scalar function in the…

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Q: Compute the directional derivative of the function f(x,y, z) = 3ryz at the point P: (1, –3, –1) in…

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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: Given f(x,y,z) = x2 + y2 + z2, find the maximum value of the directional derivative (df/ds) at the…

A: Consider the provided question,

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

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

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (19, 5, -1)

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

Q: Let f(x, y, z) = 3xy + 2yz - xz. Find the directional derivative of f(x, y, z) in the direction of…

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

A: Here we will find out the required value.

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

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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: 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: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i…

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Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

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

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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)

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

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Q: Find the gradient of the function at the given point. w - x tan(y + z), (8, 5, –2) Vw(8, 5, –2) =

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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: Use the gradient to find the directional derivative of the function at P in the direction of PQ g(x,…

A: Given that: g(x, y, z)=xye10z,     P(4, 12, 0), Q(0,0,0)

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

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

A: Given that, the function is gx,y,z=xye8z and the points are P3,12,0 and Q0,0,0.…

Q: For function f (x, y) x²+1 Find the directional derivative of f at the point (1,2) in the direction…

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