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- Find the gradient vector field of the function f(x, y) = //e-6 6x F(x,y) = 02 Find the gradient vector of the function f(x, y) = exy - x² at the point (1,1).The gradient vector field of f(x,y)=y(2x2 -y3 ) is given by: O1. (2xy)i +(x2 -3y² )i O II. (4xy)i -(2x2 -3y? )i O II (4xy)i +(4x2 -3y² )i OV. (4xy)i +(2x2 -3y² )i
- Find the gradient fields of g(x, y, z) = xy + yz + xzLet R be a differentiable vector-valued function such that R'(t) = (3t2,2tvt? + 1, 2t + 3) and R(1) = (4, *2, 3). Find R(0).Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the direction vector (2, -1, −2):