Switching partial and ordinary derivatives

[Nusc]

Homework Statement

F(q_1,...,q_n,t)

$$\frac{d}{dt}\frac{\partial}{\partial \dot{q}} \frac{dF}{dt} = \frac{\partial}{\partial q} \frac{dF}{dt}= \frac{\partial}{\partial t}\frac{\partial}{\partial q} +\frac{\partial}{\partial q}\frac{\partial}{\partial q} \dot{q}$$

What's the theorem for switching partial and ordinary derivatives?

Homework Equations

The Attempt at a Solution

 

[DrMath]

Laplace Transform?
Don't quite get what u mean :P