The derivative of $e^x$ We all know that the derivative of $e^x$ equals $e^x$.
I found this notation on Wikipedia: 
$$\dfrac{d}{dx} e^x = e^x$$
Why isn't this expression $$\dfrac{dy}{dx} e^x = e^x$$
Is it because $$\dfrac{d}{dx} e^x = \dfrac{d \space e^x}{dx}  $$
I'm asking this because I have only encountered $\dfrac{dy}{dx}$ when differentiating (mainly because I always use the $f'(x)$ method.
 A: Here $y=e^x.$  That's why $\dfrac{dy}{dx}=\dfrac{d(e^x)}{dx}.$ However if write down $\dfrac{dy}{dx}e^x$ it simply means $e^x\times \dfrac{dy}{dx}.$
A: It's really hard to talk students out of writing $\dfrac{dy}{dx}f(x)$ when the mean $\dfrac{d}{dx} f(x)$ or $f'(x^3)$ when they mean $\dfrac{d}{dx} x^3$.
If $y=f(x)$ then $\dfrac{dy}{dx}$ is the same as $\dfrac{df(x)}{dx}$, and this may also be written as $\dfrac{d}{dx}f(x)$.  But $\dfrac{dy}{dx} f(x)$ means something different: It means you're multiplying $\dfrac{dy}{dx}$, which is a function of $x$, by $f(x)$.
A: Some write $y=f(x)$. then $y$ is a function of $x$ and you can
talk about $\frac{d}{dx}y$ which also has the notation $\frac{dy}{dx}$.
$\frac{d}{dx}f$ is a notation for the derivative of $f$ with respect
to $x$, $f$ is a function of $x$.
So if $y=f(x)$ then $$\frac{d}{dx}f=\frac{d}{dx}y=\frac{dy}{dx}$$
A: Let's untangle the notations you're combining.
$\dfrac{d(e^x)}{dx} =\dfrac{d}{dx} e^x$ indicates that you're taking the derivative of $e^x$. Normally, nobody uses the first version when the thing differentiated is more complicated than a single letter.
$\dfrac{dy}{dx}=\dfrac{d}{dx}y$ indicates you are taking the derivative of $y$, whatever that is.
Now if $y=e^x$, then $\dfrac{dy}{dx}= \dfrac{d}{dx} e^x $  means the same thing.
A: Leibniz composed different notations
some of them are 


*

*$\Large \frac{dy}{dx}$-here we need to know $y=f(x)$,


whilst in the following notations we have this in the symbols


*

*$\frac{d}{dx}f(x)$


$D_x[f(x)]$
notice that
$\large \frac{dy}{dx}e^x$
is a product of two quantities
the 
$\frac{dy}{dx}=f'(x)$ and an arbitrary function $e^x$
