If f is a function of $x$ and $t$ where $x$ itself is a function of time does this mean $\frac{\partial f}{\partial x}=0$?

Question

$\frac{\partial f(x(t),t)}{\partial x}=0$?

I suspect it probably doesn't but I can't justify it to myself.

score 2 · Answer 1 · answered Jan 23 '14 at 23:18

2

Hint: $$ \frac{\partial f(x(t),t)}{\partial x}=\frac{\frac{\partial f(x(t),t)}{\partial t}}{\frac{\partial x(t)}{\partial t}} $$

answered Jan 23 '14 at 23:18

Arash

11,131

score 0 · Answer 2 · answered Jan 23 '14 at 23:48

0

The equation $$\frac{\partial f}{\partial x} =0$$ means that $f$ has no dependence on its first variable. Thus $f(x_1,t)=f(x_2,t)$ for all possible values of $x_1,x_2,t$.

answered Jan 23 '14 at 23:48

user1337

24,381

If f is a function of $x$ and $t$ where $x$ itself is a function of time does this mean $\frac{\partial f}{\partial x}=0$?

2 Answers2