Applying Chain Rule to a function of two variables

[Dilemma]

Hello,

Here is the question:

I can not figure out how we are to apply chain rule to the second order derivative. May somebody clarify that?

 

[TJGilb]

Do you know how to solve this if it were only asking you to find $\frac {d\omega} {dt}$?

 

[Dilemma]

Yes, I do know that.

 

[TJGilb]

Unfortunately it's late for me and I don't have time to go into this right now. But here is another thread on this topic that may be of use https://www.physicsforums.com/threads/chain-rule-for-2nd-derivatives.492937/