Vector Diff. Q: Dot & Cross Prod. Differentiation?

[sams]

I have a question regarding the dot product and the cross product differentiation. I was wondering whether:
$$\frac{d(\vec{A}.\vec{B})}{du} = \vec{A}. \frac{d\vec{B}}{du} + \frac{d\vec{A}}{du} .\vec{B}$$
is the same as
$$\frac{d(\vec{A}.\vec{B})}{du} = \frac{d\vec{A}}{du} .\vec{B} + \vec{A}. \frac{d\vec{B}}{du}$$

and
$$\frac{d(\vec{A}×\vec{B})}{du} = \vec{A}× \frac{d\vec{B}}{du} + \frac{d\vec{A}}{du} ×\vec{B}$$
is the same as
$$\frac{d(\vec{A}×\vec{B})}{du} = \frac{d\vec{A}}{du} ×\vec{B} + \vec{A}× \frac{d\vec{B}}{du}$$

or not!

Thank you so much for your help...

 

[DrClaude]

Addition is commutative even with vector elements, so yes, all equalities you wrote hold.

 

[sams]

Addition is commutative even with vector elements, so yes, all equalities you wrote hold.

Thank you DrClaude for your reply and for your help