# Second derivative

In physics and mathematics, the second derivative is the derivative of the derivative of a function, say ${\displaystyle f(x)}$. 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

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

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 ${\displaystyle f(x)=x^{n}}$, then the second derivative of the function can be found using the power rule for second derivatives

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