University Mathematics Handbook (2015)
IX. Vector Analysis
Chapter 4. Properties of the Derivatives
4.1 Derivative Rules
If 
, 
are derivable vector functions, 
a constant vector and 
a scalar function, then:
1. 
2. 
3. 
4. 
5. 
6. If is a vector function of constant length 
, then is perpendicular to 
.
4.2 Lagrange's Mean Value Theorem
If vector function 
is continuous in the neighborhood of 
and has a continuous derivative on , then there exists 
of that neighborhood where:
when 
is a vector function holding 
.