Product rule for the Laplacian

For twice differentiable scalar fields,

\nabla^{2} (f g) = f \nabla^{2} g + 2\nabla f \cdot \nabla g + g \nabla^{2} f .

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Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 76 / 5 / Solution
Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 37A / b / i / Solution

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