- #1
Hassan2
- 426
- 5
Dear all,
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 Euler–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.
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 Euler–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.