For the function f(x,y, z) := 10r + 7y³ + 723 + 9ry + 6yz+ 12rz+ 19 find the gradient at the point (1, 1, 1): Vf(1,1,1) = ( Find the directional derivative off at the point (1,1,1) in the direction of the vector (6, 3,6): Notice that you might need to normalize the vector (6, 3, 6). To derivate in the direction of a given vector means to derivate along the unit vector pointing in the same direction.

Q: (a) Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change…

A: The given function f(x,y,z)=xy+yz2+xz3, P(2,0,3)u=-23,-13,23

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: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

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Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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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: f(x, y, z)=1/√√√x² + y² + z² P(-1,2,2) = -3i+27-3k

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Q: 14. Domain of /og

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Q: 2yz - 2yz2 + x at the point p = (1, -1, 1), find the unit vector that indicates the direction in…

A: Introduction:   The gradient of the temperature function at the point is the direction of the…

Q: The cost C in dollars of manufacturing x bicycles at a production plant is given by the function…

A: topic- application of derivatives

Q: The directional derivative of the function f(x, y, z) = x³y4 – 3z2 at the point (1, 1,1) in the…

A: we have to find the directional derivative

Q: Find the derivative of the vector function r(t) = ta x (b+ tc), where a = (4, -1,5), b = (-3,-3,-1),…

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…