Find the Correct Identity, If $f$ Is a Scalar Field $\mathbf { F }$

Multiple Choice

Find the correct identity, if $f$ is a scalar field, $\mathbf { F }$ and $\mathbf { G }$ are vector fields.

A) $\operatorname { div } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f$
B) $\quad \operatorname { curl } ( f \mathbf { F } ) = f \operatorname { div } ( \mathbf { F } ) + \mathbf { F } \cdot \nabla f$
C) $\operatorname { div } ( f \mathbf { F } ) = f \operatorname { curl } ( \mathbf { F } ) + ( \nabla f ) \times \mathbf { F }$
D) None of these