How is the differentiation of a vector sum performed?

[FOIWATER]

I know how to differentiate the dot and cross products of two vectors, is the differentiation of a vector sum done like this:

d/dt (u+t) = u' + t + u + t'

Or simply add them and then differentiate?

Thanks

 

[Muphrid]

(u+t)'=u'+t', as it is for scalar functions. This is linearity.

 

[FOIWATER]

thanks