a) Compute the gradient of the function f(x, y, z) = e*y² . b)Compute the directional derivative Daf (1, 2, 3), where 1 1 2 2 2 c)Let p(t) be a parametric curve with P(7) = (1, 2, 3), (7) = (-2,5, 3). Compute the derivative (fop)(7).

Q: A function z=f(x, y) is defined implicitly by the equation xy2 - x²z+yz² -z = 11 near point (2, -2,…

A: Given function is fx, y, z = xy2-x2z+yz2-z-11

Q: 4. (a) Determine the directional derivative of f(x, y, z) = zety at the point (1, −1, 1) in the…

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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: 3-find the gradient of the function v if_w=(xy)/z at the point(1,-2,1), find the directional…

A: The answer provided below has been developed in a clear step by step manner.

Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

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Q: f(x,y,z)=5sin(xyz), (a,b,c)=(1,1,π/4), and v⃗ =(3,-√2,3). Calculate the directional derivative…

A: Here we will evaluate each expression.

Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: 3. Find the directional derivative of f(x, y) = cos(3x+4y) at the point (7/6, π/6) along the…

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Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

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Q: Let f(x, y) = x²y + y²x. Find the directional derivative at (-3, 2) in the direction = π/2.…

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Q: Choose the gradient of f(x, y) = x²y³. (a) 2xi +3y²j, (b) (c) 2xy³i+3x²y²j, (d) x²i+y³j, y³i+x²j.

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