(9) Determine whether or not the vector field is conservative. If it is conservative, find a function f such that F = Vf. I F(x, y) = (cos x+sin y+y sec² ry-2x+y²-2xy², 2y+2xy-2x²y+r sec² ry+r cos y)

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6. Denote by V the vector ·(). Then we can define the operations grad (f) = f (gradient of f), div (F) = V F (divergence of F), and curl (F) = ▼ × F (curl of F). (a) Given F = (2x + 3y, 3x + z, sin x), calculate div(F) and curl(F). (b) Is the vector field F = (x + y,3y, z-x+1) conservative? What about F = (yz, xz, xy)? (c) Calculate V × (Vf) =curl(grad f) and V. (V × F) = div(curl F).