Calculate the gradient, Vƒ, for the following scalar functions (a) ƒ = xyz. (b) ƒ = x² + y² + z². (c) f = xy + yz + xz.

Q: Consider a function f: R? → R°, the derivative of f isa O 3 x 3 matrix O 3 x 2 matrix O 2 x 3 matrix…

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Q: Find the gradient of the function at the given point. g(x, y) = 3xe/x, (10, 0) Vg(10, 0) = 3i + 3i

A: g(x, y)= 3 x eyx∇g(x, y) =∂g∂x, ∂g∂y∂g∂x=3eyx+3x eyx-yx2      =3eyx 1-yx∂g∂x=3eyx (x-yx)∂g∂y=3x1x…

Q: Choose the gradient of the function : f(x, y) = ex² Select one: O None of these ○ (6ye+²+³y², 2xer²…

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

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Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

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A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Sketch a contour map of the function. f(x, y) = x² + 7y² y

A: The given function is .To determine the contour map and the sketch of the function.

Q: Find the gradient of the following function. 3 f(x, у) %3 5x° - ху Vf(x, y) =

A: Gradient of f(x,y) is given by∇f(x , y) = i⇀ ( fx ) + j⇀( fy )

Q: Find the directional derivative of f(x, y) = sin(x+2y) at the point (-3, 5) in the direction = π/6.…

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Q: Find the gradient function for: 21y-

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Q: Round each component to four decimal places, if necessary. Find the gradient of f(x, y) = 4e³x/y +…

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Q: Find the gradient of f (x, y) = 2xy² – 3x°y.

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Q: Suppose f (x, y) = , P = (-2, -1) and v = 2i - 4j. A. Find the gradient of f. (Vƒ)(x, y) =i+j Note:…

A: Since you have posted a question with sub-parts greater than three. We will provide the solution…