Proof of dy=f’(x)dx I’ve been wondering about the usage of $dy=f’(x)dx$ in my textbook.
There’s not a single justification of how it is proved and it just states that it is true.
Since $dy/dx$ can’t be assumed as a fraction, I’m guessing there’s more to it than just multiplying by $dx$ on both sides.
Are there any proofs to this equation? 
Also with some research, I found this “proof”. Can it be done this way?
$dy=f’(x)dx$ “proof”
(Please keep this in high school level)

Well the derivative is given by:
$$\lim_{dx \to 0} \frac{f(x+dx)-f(x)}{dx}=\lim_{dx\to 0} \frac{dy}{dx}$$
By definition the derivative is the rate of change of y with regard to x. That's why RHS stands. As you realise $\frac{dy}{dx}$ is not just a notation but it's mathematically how derivative is been defined. Since $f'(x)=\frac{dy}{dx}$ with $dx\to 0$, the equation $dy=f'(x)dx$ holds.
