Mathematics · University
Divergence of a polynomial vector field
Match each component to its own coordinate derivative.
Method and conditions
Match each component to its own coordinate derivative.
div F = ∂F₁/∂x + ∂F₂/∂y + ∂F₃/∂z
Worked examples
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
For F = (3x², 8y², 8z²), find div F at (3,4,-2). Round the final result to 4 decimal places if needed.
Differentiate componentwise: div F = 6x + 16y + 16z.
50
Try it
For F = (5x², 8y², 7z²), find div F at (2,-3,2). Round the final result to 4 decimal places if needed.
For F = (5x², 12y², 5z²), find div F at (3,-2,3). Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 0
Differentiate componentwise: div F = 10x + 16y + 14z.
- 12
Differentiate componentwise: div F = 10x + 24y + 10z.
Further reading and review references
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