- Calculus, Volume 1: One Variable Calculus, with an Introduction to Linear Algebra
- Tom M. Apostol
- Second Edition
- 1967
- 978-1-119-49673-1
14.4 Exercises
- If $G = F \times F',$ compute $G'$ in terms of $F$ and derivatives of $F.$
- Use the cross product identity from Theorem 14.1:$$(F \times G)' = F' \times G + F \times G'$$and recall from section 13.9 that $A \times B = O$ if and only if $A$ and $B$ are linearly dependent.
- Using the cross product identity from theorem 14.1: $$(F \times F')' = F' \times F' + F \times F''$$And since F' is linearly dependent to itself, $F' \times F' = O,$ giving us $$G' = F \times F''\quad\blacksquare$$