Divergence Practice

Calculus Level 1

What is the divergence of the vector field F ⃗ = ⟨ x y , y z , z x ⟩ ? \vec{F} = \left \langle xy,yz,zx \right \rangle ?

x y z xyz x + y + z x+y+z x y + y z + z x xy+yz+zx x + y x+y

Matt DeCross by Matt DeCross , 27, USA

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1 solution

展豪 張
Mar 22, 2016

∇ ⃗ ⋅ F ⃗ = ∂ ∂ x ( x y ) + ∂ ∂ y ( y z ) + ∂ ∂ z ( z x ) = y + z + x = x + y + z \displaystyle\vec\nabla\cdot\vec F=\frac\partial{\partial x}(xy)+\frac\partial{\partial y}(yz)+\frac\partial{\partial z}(zx)=y+z+x=x+y+z

2 Helpful 0 Interesting 0 Brilliant 0 Confused

This was pretty straightforward. I wonder what the graph looks like. Also, does any combination of a product of 2 variables give the same answer?

Aisthu Lucky - 2 years, 2 months ago

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