∇⋅(Aρ^+Bθ^+Cφ^)=1ρ2∂∂ρ(ρ2A)+1ρsinθ∂∂θ(sinθB)+1ρsinθ∂∂φ(C)\nabla\cdot (A\hat{\rho}+B\hat{\theta}+C\hat{\varphi})=\frac{1}{\rho^{2}} \frac{\partial}{\partial\rho}(\rho^{2}A)+\frac{1}{\rho\sin\theta} \frac{\partial}{\partial\theta}(\sin\theta B)+\frac{1}{\rho\sin\theta} \frac{\partial}{\partial\varphi}(C)∇⋅(Aρ^+Bθ^+Cφ^)=ρ21∂ρ∂(ρ2A)+ρsinθ1∂θ∂(sinθB)+ρsinθ1∂φ∂(C)∇⋅(Aρ^+Bθ^+Cφ^)=1ρ2sinθΔθΔφ∂∂ρ(ρ2sinθΔθΔφA)+1ΔρρsinθΔφ∂ρ∂(θ)(ΔρρsinθΔϕB)+1ρΔθΔρ∂ρsinθ∂(φ)(ρΔθΔρC)\nabla\cdot (A\hat{\rho}+B\hat{\theta}+C\hat{\varphi})=\frac{1}{\rho^{2}\sin\theta\Delta\theta\Delta\varphi} \frac{\partial}{\partial\rho}(\rho^{2}\sin\theta\Delta\theta\Delta\varphi A)+\frac{1}{\Delta\rho\rho\sin\theta\Delta\varphi} \frac{\partial}{\rho\partial(\theta)}(\Delta\rho\rho\sin\theta\Delta\phi B)+ \frac{1}{\rho\Delta\theta\Delta\rho}\frac{\partial}{\rho\sin\theta\partial(\varphi)}(\rho\Delta\theta\Delta\rho C) ∇⋅(Aρ^+Bθ^+Cφ^)=ρ2sinθΔθΔφ1∂ρ∂(ρ2sinθΔθΔφA)+ΔρρsinθΔφ1ρ∂(θ)∂(ΔρρsinθΔϕB)+ρΔθΔρ1ρsinθ∂(φ)∂(ρΔθΔρC)
