# Vector Differentiation

• I
Gold Member
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...

Last edited:

## Answers and Replies

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

sams
Gold Member
Addition is commutative even with vector elements, so yes, all equalities you wrote hold.
Thank you DrClaude for your reply and for your help