What is the gradient field associated with the potential function f(x,y,z) = 3x2+8y2z3

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

Show that the force F= (-6x +*yz IS Conservative, hence Find the Potential function to

Find the gradient field of the function g(x,y,z) = 8xy + 7yz + 9xz.

2 Find the gradient vector of the function f(x, y) = exy - x² at the point (1,1).

Find the gradient vector field of f(x,y)=ln(6x+y)

- 1/2 Find the gradient field of the function, f(x,y,z) = (2x² + 2y² +2²)

Find the gradient field of the function g(x,y,z)=9xy + 3yz + 8xz. Vg= (Type your answer in terms of i, j, and k.)

Find a potential function for the vector field .F(x,y)=<16xy+8y-2,8x^2+8x>