The gradient of scalar field U = ρ 2 z cos (2ϕ) is:

10 sin 2 θ.cos (ϕ)r̂ + 10 sin (2θ) cos (ϕ) θ̂ - 10 sin θ sin (ϕ) ϕ̂

2ρz cos (2ϕ)ê + 2ρz sin (2ϕ) ϕ̂ + ρ 2 cos (2ϕ)ẑ

2ρz cos (2ϕ) ê - 2ρz sin (2ϕ) ϕ̂ + ρ 2 cos (2ϕ)ẑ

The gradient of scalar field U = ρ²z cos (2ϕ) is:

10 sin²θ.cos (ϕ)r̂ + 10 sin (2θ) cos (ϕ) θ̂ - 10 sin θ sin (ϕ) ϕ̂

2ρz cos (2ϕ)ê + 2ρz sin (2ϕ) ϕ̂ + ρ² cos (2ϕ)ẑ

2e^-z cos 2x coshy x̂ + e^-z sin 2x sinhy ŷ - e^-z sin 2x coshy ẑ

2ρz cos (2ϕ) ê - 2ρz sin (2ϕ) ϕ̂ + ρ² cos (2ϕ)ẑ