The difference between $\Delta x$, $\delta x$ and $dx$ $\Delta x$, $\delta x$ and $dx$ are used when talking about slopes and derivatives. But I don't know what the exact difference is between them.
$\Delta x$ is about a secant line, a line between two points representing the rate of change between those two points. That's a &quot;differential&quot; (between the two points).
$dx$ is about a tangent line to one point, representing an instantaneous rate of change. That makes it a &quot;derivative.&quot;
$\delta x$ is about a tangent line to a partial derivative. That's a rate of change or derivative in one direction, holding a number of other directions constant.
$∆x~$ is small change in $~x~$.

$~dx~$ is small part of $~x~$ but represents independent change. 
&amp; $~\frac{dy}{dx}~$ means slope of tangent at a point where it touches to the curve 
$~\frac{∆y}{∆x}~$ s the slope through two points.

We say $~∆x~$ tends to zero .

It becomes $~\frac{dy}{dx}~$  which is slope of tangent at a point (reason of why $~∆x~$ tends to zero).

That is it