Just thought I'd add another note as to how the notation comes about. why is it squared if it just means we do it twice? here's why.
as i explained before, d/dx means to find the first derivative with respect to x.
example, d/dx (x^2) = 2x
when we find the second derivative, what we do is find the derivative of the first derivative, and so we apply one notation after the other.
example, find the second derivative of x^2
d/dx [d/dx (x^2)] = (d/dx)^2 (x^2) = (d^2/(dx)^2) (x^2) = 2
so you see we applied the derivative twice and hence got the square, since derivative notations possess the property of being able to be manipulated like fractions.