Cross product (?) derivative

[ch0c0]

Greetings good people of the math help board!

I apologize if this seems trivial to some of you but I'm somewhat stuck. I need to find a derivative of the 3D point-to-line distance function. So the function is as follows:


3D points:
a => lies on the line
p => point to find the distance to the line for
Vectors:
v => directional vector for the line that contains point a
p-a => vector from point a to point p

distance = length( p-a crossP v) / length(v)

I understand that a derivative of the cross product is obtained as follows (and feel free to correct me if I'm wrong here):

(p-a crosP v)' = p-a crossP v' + (p-a)' crossP v

However, I'm not clear on how to do this when the components are vectors. I mean, if I take a derivative of each of the vectors they'd be just 0's :?

Also, presuming I've managed to successfully obtain the derivative of the cross product, should I also write out/calculate the derivative of the enclosing functions i.e.: for each of the lengths and the division?

Thank you in advance

C.

 

[ch0c0]

Hi again,

As there appears to be no takes on any semblance of an answer, could some one please at least tell me if this is impossible or completely incorrect to even thing about this way?

Thanks.