Derivative in spherical coordinates

[williamcarter]

Homework Statement

-here is the problem statement

-here is a bit of their answer

Homework Equations

Chain rule, partial derivative in spherical coord.

The Attempt at a Solution

I tried dragging out the constant and partial derivate with respect to t but still I can't reach their df/dt and d^2f/dt^2 partial derivatives.
Any help would be much appreciated.
Thank you !

 

[haruspex]

Homework Statement

View attachment 109867 -here is the problem statement

View attachment 109868 -here is a bit of their answer

Homework Equations

Chain rule, partial derivative in spherical coord.

The Attempt at a Solution

I tried dragging out the constant and partial derivate with respect to t but still I can't reach their df/dt and d^2f/dt^2 partial derivatives.
Any help would be much appreciated.
Thank you !

Please post your attempts anyway.