Vector Differentiation

  • #1
sams
Gold Member
84
2

Main Question or Discussion Point

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

  • #2
DrClaude
Mentor
7,148
3,283
Addition is commutative even with vector elements, so yes, all equalities you wrote hold.
 
  • #3
sams
Gold Member
84
2
Addition is commutative even with vector elements, so yes, all equalities you wrote hold.
Thank you DrClaude for your reply and for your help
 
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