## Differentiating Vectors

Theorem

Ifandare vectors, both functions of time, then

1.

2.

3.

4.

5. Ifthenconstant vector.

Proof

Ifthen

1.

2.

3. Let

Hence

Asand so

4. Ifthen writing

Integrating compents one at a times givesare constant andis a constant vectors.