Vector differentiation

r = l dx
A ^ p r/ p theta

partial derivative of r when observed from reference frame A with respect to theta

p r/ p theta is meaningless if no frame is given!

If theta, beta, alpah, l are all themselves functions of time
-> theta(t), beta(t), alpha(t), l(t), time t is the single variable

r(t) = a1(t)ax + a2(t)ay + a3(t)az

A^ d r / dt = da1 / dt * ax + ...

use dot notation 

when the measure numbers are expressions containing implict functions of time, eg theta(t), the chain role can be used to calculate the derivative.

A ^ dr /dt = A ^ (p r / p theta) * (d theta / dt) + A ^ (p r / p beta) * (d beta / dt) + ...

if t is explict in expressions 最后要加上 A ^ (p r / p t) 

Second (and higher) derivatives