- #1
yungman
- 5,718
- 241
Let [tex] \vec w(t) \;,\; \vec v (t) [/tex] be 3 space vectors that is a function of time t. I want to verify that:
[tex] \frac {d(\vec w \cdot \vec v)}{dt} = \vec v \cdot \frac { d\vec w}{dt} \;+\; \vec w \cdot \frac { d\vec v}{dt} [/tex]
I work through the verification by splitting w and v into x, y, z components, do the dot product and take the derivative to verify already. Just want to run this by the expert to confirm.
Thanks
Alan
[tex] \frac {d(\vec w \cdot \vec v)}{dt} = \vec v \cdot \frac { d\vec w}{dt} \;+\; \vec w \cdot \frac { d\vec v}{dt} [/tex]
I work through the verification by splitting w and v into x, y, z components, do the dot product and take the derivative to verify already. Just want to run this by the expert to confirm.
Thanks
Alan