What does it mean to do something like $ \frac{dx}{dx} x$ rather than just $ \frac{d}{dx} x$ ?

Question

solomonzelman · Answer

$\color{#000000 }{ \displaystyle dy/dx  }$ = you're differentiating the function $\color{#000000 }{ \displaystyle y  }$, with respect to $\color{#000000 }{ \displaystyle x }$.

$\color{#000000 }{ \displaystyle \frac{dx}{dx}  }$ = you're differentiating x with respect to x. (d/dx of x is 1).

So, $\color{#000000 }{ \displaystyle \frac{dx}{dx}x  }$,
would likely be determined as:
$\rm «$the derivative of x with respect to x, times x$\rm »$.

solomonzelman · Answer

I haven't ever seen anyone use: $\color{#000000 }{ \displaystyle \frac{dx }{dx} x }$

I'm sure enough that this is wrong.

solomonzelman · Answer

Where as  $\color{#000000 }{ \displaystyle \frac{d }{dx} x }$ = derivative of x with respect to x.

doughnuttable · Answer

Is $\frac{dy}{dx}$ the same as $\frac{d}{dx} y$?

solomonzelman · Answer

Yes, that is same, I think.
Both mean, $«{\tiny~}$the derivative of $y$ with respect to $x$${\tiny~}»$.