Vector Calculus

(A.63) |

When written out in component form this becomes

(A.64) |

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

(A.65) |

which implies that

(A.66) |

Moreover, it is easily demonstrated that

(A.67) |

and

(A.68) |

Hence, it can be seen that the laws of vector differentiation are analogous to those in conventional calculus.