Find a potential function for the vector field F(x, y) = (6x sin y,3 cos x), if it exists %3D A. No potential function exists B. (x,y) = (3x² sin y, 3 cos xy) %3D C. p (x, y) = 18x cos x sin y D. (x, y) = 3x² sin y + C(y) %3D E. o (x, y) = 6 sin y %3D

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A: Apply chain rule

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A: Given that  f(x,y,z)=x^2-(1-y)^2+z^2 Point P(1,1,1) Vector is a=(0,3,4)  To find the directional…

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A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: 1. Compute d e (z²) (sin(t) + e*)v= dr

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Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

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A: Solution:-

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²* sin(5y)j + z5k. f(x, y, z) =

A: The given gradient function

Q: af If f(x,y) = sin-(4x³y?) then dx 12x?y? 1-(4x³y²)² O a. b. 1 4x³y²/(4x³y?)² – 1 c. 12x²y² 4x³y?…

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Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

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A: GIVEN

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