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Suppose that vector varies with time, so that
. The time
derivative of the vector is defined

(38) 
When written out in component form this becomes

(39) 
Suppose that is, in fact, the product of a scalar and another vector
. What now is the time derivative of ? We have

(40) 
which implies that

(41) 
It is easily demonstrated that

(42) 
Likewise,

(43) 
It can be seen that the laws of vector differentiation are fairly analogous to those in
conventional calculus.
Next: Line Integrals
Up: Vectors
Previous: The Vector Product
Richard Fitzpatrick
20070714