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Multivariable Calculus

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Divergence of Cross Product of Gradients

MVCALC-JMA4LG

Let $f$ and $g$ be twice differentiable functions defined in $\mathbb{R}^3$, all the second order partial derivatives are continuous. Calculate the following expression:

$$\text{div }(\nabla f \times \nabla g)$$

A

$0$

B

$1$

C

$-1$

D

$\pi$

E

$2\pi$