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I have a confusion about partial derivatives.

Say I have a function as

[itex]y=f(x,t)[/itex]

and we know that

[itex]x=g(t)[/itex]

1. Does it make sense to talk about partial derivatives like [itex]\frac{\partial y}{\partial x}[/itex] and [itex]\frac{\partial y}{\partial t}[/itex] ?

I doubt, because the definition of partial derivative is the change in the function due to the change on the selected variable ( other variables are kept constant).

2. If it does not make sense, then how in Eulerâ€“Lagrange equation we use the partial derivatives with respect to a function(x(t)) and its derivative(x'(t)) while they depend on one another.

Your help would be appreciated.

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# Confusion about partial derivatives

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