Derivative of a vector expression?

[quarky2001]

I'm trying to find the time derivative of the following function, where E is a constant, spatially uniform vector field, and B is as well, but B varies with time.

<br /> \frac{d}{dt}\left(\frac{\vec{E}\times\vec{B}}{B^2}\right)<br />

Remembering that B is time dependent and E is not, I've calculated the derivative of this as (where a dot above the letter indicates a time derivative):

<br /> \frac{1}{B^4}\left[B^2(\vec{E}\times\dot{\vec{B}})-2B\dot{B}(\vec{E}\times\vec{B})\right]<br />

Can anyone tell me if this is correct?

 

[Dick]

That looks fine to me, assuming you mean a dot product between B and its derivative.

 

[quarky2001]

Whoops, forgot that! Thanks for checking it though. It's a shame it doesn't simplify more, but so long as it's correct I'm fine with it.