Mathematics · University
Divergence of a polynomial vector field · formula reference
Match each component to its own coordinate derivative.
Formula
Match each component to its own coordinate derivative.
div F = ∂F₁/∂x + ∂F₂/∂y + ∂F₃/∂z
Worked example
For F = (10x², 12y², 4z²), find div F at (2,0,1). Round the final result to 4 decimal places if needed.
Differentiate componentwise: div F = 20x + 24y + 8z.
48
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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