TITLE: Second derivative symbol $\frac{d^2y}{dx^2}$!
QUESTION [6 upvotes]: I'm currently studying taking the second derivative of equations and I have been told the symbol used to represent second derivative is 

$$\frac{d^2y}{dx^2}$$

I was just wondering, why this symbol is chosen? Why is it not $$\frac{dy^2}{dx^2}$$ or $$\frac{d^2y}{d^2x}$$

REPLY [2 votes]: $$ y'=\frac {d}{dx}(y)=\frac {dy}{dx} $$
$$ y''=\frac {d}{dx}(\frac{d}{dx}y)=\frac {d^2y}{dx^2} $$
$$ y'''=\frac {d}{dx}(\frac {d^2}{dx^2}(y))=\frac {d^3y}{dx^3}$$