Assume that f(r, y) is a function given by if (r, y) # (0,0), f(r, y) = 0 if (r, y) = (0, 0).

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 direction at which the function f(x, y, 2) = a In(e-az) increases fastest at (-3,0, 0) O…

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Q: What is the directional derivative of f(x, y, z) = bx²y²z² + x² + y² + z² in the direction of v =…

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Q: Find the gradient of the function at the given point.

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Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx at the point (1,-1,1) in the direction…

A: Directional derivative using gradient

Q: Let f(x, y) = . Use the Linear Approximation at an appropriate point (a, b) to estimate…

A: Given,f(x,y) = x2y2+1To estimate,f(4.02,0.93) using the LinearApproximation at an appropriate point…

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

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

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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 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: Find the direction at which the function f(x, y, z) = x In(e – az) increases fastest at (-3,0, 0) O…

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Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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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: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: The gradient of f(æ, y) = e3 * sin(2 · y) at (2, y) = (3, – 2) is defined as followed: V f(æ, y) =…

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Q: Find the direction at which the function f(x, y, z) increases fastest at (2, 0, 0) = x In(e' – xz)…

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Q: Let f(x, y, 2) =x² + 3r°y? + 2°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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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 derivative of the function f (x, y, z) = -9x + 5y – 10z at the point (-3, 6, 5) in the…

A: we have to find the following . I have explained in details please see the explanation and if any…

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Find the derivative of the function at P0 in the direction of u. f(x, y, z) = -9x + 3y + 8z, P…

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Q: Let f(x, y) = (x° + ay´, xʻy°, 2x+by), g(u,v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: f(x,y)=(x3+ay2,x2y3,2x+by)g(u,v,w)=(3u2+bv2+w3,uvw)To Find: Derivative of f(g(u,v,w)) using the…

Q: Find ( fx fy, fzf xy f yx fxyz f zzx) for the function: f(x, y, z) = xyz + x²y + z³x + x²y?

A: To find the differentiation of the function

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: 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: Find the linearization of f(x, y) = −x² + 2y² at the point (3,-1). Use the linearization to estimate…

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Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: Determine D,f(3,-1,0)for f(xy.z) = 4x-y'e in the direction of i = (-1,4,2, (Express your final…

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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) =

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

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Q: Find the directional derivative of F(x , y , z)=7y2e−x+3z2 in the direction u=(3,6,−2) at the point…

A: We have to solve

Q: Let f(1,y) = (r+ay°,r²y°,2r + by), g(u, v,w) = (3u² + bv² + w°, uvw). Find the derivative of…

A: Let f(x, y)=x3+ay2, x2y3, 2x+by,  gu, v, w=3u2+bv2+w3, uvw. We need to find the derivative of fgu,…

Q: Find the linearization of f(x,y) at the indicated point (X0,Yo): f(x,y) = In (x² + y); (1, 1) L(x,y)…

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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 at the given point. f(x, y) = 2x + 4y² + 4, (3, 4) Vf(3, 4) =

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Q: Let f (z) = (7z + 9) (i – z). What is the real part of the derivative f' (1+ i)?

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

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Q: 2 - What is the directional derivative of the function f(x, y, z) = x° - 2xy + z point A, = (1,1,0)…

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Q: Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1, 2).

A: Evaluate : ∫∫T(x-y)dA        ......(1) ∫∫Tx-ydydx T is the region enclosed by the triangle. Region…

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: Use the definition of directional derivative to solve Duf(xo, yo, zo) at point P(xo, yozo) where…

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

Q: Compute the gradient for the function f (x, y) = 4x² – 9y at the point (10, -9) %3D

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Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Find the direction in which the function f (x, y, z) = xy - In z is increasing most rapidly at the…

A: We will use directional derivative here

Q: If f(x,y,z)=xe^(2y)sin(8z), then the gradient is ∇f(x,y,z)=

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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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