One of the problems ([#7](https://nptel.ac.in/content/storage2/courses/112103167/module2/lec16.pdf#page=6)) in the following notes appears to suggest that

$
\nabla \, \times ( {\bf u} \times {\bf v} ) = (\nabla . {\bf v}) \, {\bf u} - (\nabla {\bf v}) \, {\bf u}
$

(it is the second term that I am struggling with), instead of

$
\nabla \, \times ( {\bf u} \times {\bf v} ) = (\nabla . {\bf v}) \, {\bf u} - (\nabla . {\bf u}) \, {\bf v} 
$

Note the second term, as suggested by the [triple vector product formula](https://en.wikipedia.org/wiki/Triple_product#Vector_triple_product). Why is the form given by author correct? If indeed it is.