University Mathematics Handbook (2015)
IX. Vector Analysis
Chapter 3. Derivative of Vector Function
a. Definition: Let us add 
to 
, then:
If the limit 
exists, then it is the derivative of vector function 
on .
b. 
c. Geometric description of 
: In this illustration, corresponds to point 
on the graph of , 
. If 
, then 
.
The limit of vector 
when , is a tangent line to graph of , at point 
. Therefore, vector 
is in the direction of the tangent line to the graph of , at .
