How to Derive Time Derivative of Spherical Unit Vectors?

[General-Simon]

Here I am doing a spherical pendulum problem, and i was asked to represent the unit vectors of spherical coor in terms of Cartesian coor, which i have already solved:
r=sinθcosφ i + sinθsinφ j + cosθ k
θ=cosθcosφ i + cosθsinφ j - sinθ k
φ= -sinφ i + cosφ j
where φ is the angle on the X-Y plane, between x and the position, and θ is between position and z

now i want to know how to process to the next step: derive the time derivative of each unit vector, in terms of spherical unit vectors.

 

[netheril96]

Just derive it
I don't know what's the problem

 

[General-Simon]

Just derive it
I don't know what's the problem

ok, Thanks, I already solved it. considering the θ and φ also as the function of t, but the unit vectors do not.