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I'm new to the language of calculus. I am learning about newtons second law and I'm trying to understand it's forms in calculus. Excuse my notation, just trying to keep it as simple as possible.

F=m * dV/dt

I know V= dx/dt

My textbook says you can 'apply chain rule' to obtain the following

dV/dt = dV/dx * dx/dt

and this becomes V * dV/dx

I'm really having trouble with grasping how the chain rule is applied here, to me when I read this it sounds like a magic wand is being waved and somehow the result above comes about. So my questions are

1) How exactly is the chain rule applied here showing the work done in the intermediate steps to get dV/dt = dV/dx * dx/dt

2) In answering 1, I hope it will answer my question of how you end up with the V at the end.