Finding Partial Derivatives with Independent Variables

[justwild]

Homework Statement

A function f(x,t) depends on position x and time t independent variables. And if \dot{f} represents \frac{df(x,t)}{dt} and \dot{x} represents \frac{dx}{dt}, then find the value of \frac{\partial\dot{f}}{\partial\dot{x}}.

Homework Equations

The Attempt at a Solution

Using the formula for total differential I can have
\dot{f} = f_{x}\dot{x} + f_{t}
Now when I proceed with differentiating partially the above equation wrt \dot{x} I am struck.

 

[Dick]

Homework Statement

A function f(x,t) depends on position x and time t independent variables. And if \dot{f} represents \frac{df(x,t)}{dt} and \dot{x} represents \frac{dx}{dt}, then find the value of \frac{\partial\dot{f}}{\partial\dot{x}}.

Homework Equations

The Attempt at a Solution

Using the formula for total differential I can have
\dot{f} = f_{x}\dot{x} + f_{t}
Now when I proceed with differentiating partially the above equation wrt \dot{x} I am struck.

Well, $f(x,t)$ doesn't depend on $\dot x$, so $f_x$ and $f_t$ don't depend on $\dot x$ either.

 

[justwild]

Well, $f(x,t)$ doesn't depend on $\dot x$, so $f_x$ and $f_t$ don't depend on $\dot x$ either.

So, I will get the answer as $f_x$. It's right.

But I didn't understand why. Can you give me a reference? I would like to read more on this.

 

[Ray Vickson]

So, I will get the answer as $f_x$. It's right.

But I didn't understand why. Can you give me a reference? I would like to read more on this.

Why do you say it is right? Is somebody telling you that?

 

[Dick]

So, I will get the answer as $f_x$. It's right.

But I didn't understand why. Can you give me a reference? I would like to read more on this.

You could look up Euler-Lagrange equations or Calculus of Variations, but the idea here is to just treat $x$ and $\dot x$ as independent variables.