The discussion revolves around the application of the chain rule in the context of second derivatives in calculus. The original poster expresses confusion regarding the formulation of the chain rule for second derivatives, seeking clarification and resources for better understanding.
The discussion is ongoing, with participants providing feedback on the original poster's attempts and questioning the assumptions behind the formulation. Some guidance has been offered regarding the application of the chain rule and product rule, but no consensus has been reached on the correctness of the expressions presented.
There is an indication of uncertainty regarding the definitions and applications of derivatives, particularly in the context of changing variables. The original poster's request for external resources suggests a potential gap in foundational understanding.
HallsofIvy said:What makes you think there is a "chain rule for second derivatives"?
Looks right. If you don't want the mixed partial, then why not apply the chain rule? After all, dx/dt' is merely a function... (Call it y, if you're having trouble thinking about it)ehrenfest said:[tex]d^2x/dt^2 = d^2x/(dt'dt) dt'/dt + dx/dt d^2t'/dt^2[/tex]?
The product rule was used. That mixed partial seems out of place. Is the above correct?