I was reading Leithold and the introduction to differentials deals with approximations, $\Delta y \approx f’(x) \Delta x$. This approximation is usable for small values of $\Delta x$.
Then the definition is made using a equality: $dy = f’(x)dx$.
Please explain this jump from $\approx$ to $=$
What do you even mean by $dy=f'(x)dx$? Can you explain what is the definition of $dx,dy$ and $f'(x)$?