Verifying Chain Rule for Partial Derivatives

[Kaguro]

Homework Statement

Given a function f(x,t) of both position x and time t, the value of $\frac {\partial \dot f}{\partial \dot x}$ where $\dot f = \frac{d f}{dt}$ and $\dot x= \frac{dx}{dt}$ is


(A) $\frac{\partial ^2 f}{\partial x^2}$

(B) $\frac{\partial f}{\partial x}$

(C) $\frac{\dot f}{\dot x}$

(A) $\frac{d f}{d x}$

Relevant Equations

None

I have no answer or solution to this. So I'm trying to seek a confirmation of whether this is correct or not:

$df = \frac{\partial f}{\partial x}dx + \frac{\partial f}{\partial t}dt$
$\frac{df}{dt} = \frac{\partial f}{\partial x} \dot x + \frac{\partial f}{\partial t}$

Therefore,
$\frac{\partial (\frac{df}{dt})}{\partial \dot x} = \frac{\partial f}{\partial x}$

 

[PeroK]

I agree with your answer, but it requires a bit of interpretation to make sense of that derivative.