- #1
Kaguro
- 221
- 57
- 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}##
##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}##