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.