Second derivative

In physics and mathematics, the second derivative is the derivative of the derivative of a function, say $f(x)$. The second derivative has many real-life applications, especially in the study of acceleration. Second derivatives can be notated in several ways, some of which are

$\frac{d^2x}{dy^2}$ or $f''(x)$

Other notations are used, but the above two are the most commonly used.

Power Rule for Finding the Second Derivative

If we have a function $f(x)=x^n$, then the second derivative of the function can be found using the power rule for second derivatives

$\frac{d^2x}{dy^2}[x^n]=(n^2-n)x^{n-2}=n(n-1)x^{n-2}$