# Notation for the Second Derivative

## Key Questions

• If you prefer Leibniz notation, second derivative is denoted $\frac{{d}^{2} y}{{\mathrm{dx}}^{2}}$.

Example:

$y = {x}^{2}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x$

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

If you like the primes notation, then second derivative is denoted with two prime marks, as opposed to the one mark with first derivatives:

$y = {x}^{2}$
$y ' = 2 x$
$y ' ' = 2$

Similarly, if the function is in function notation:

$f \left(x\right) = {x}^{2}$
$f ' \left(x\right) = 2 x$
$f ' ' \left(x\right) = 2$

Most people are familiar with both notations, so it doesn't usually matter which notation you choose, so long as people can understand what you're writing. I myself prefer the Leibniz notation, because otherwise I tend to confuse the apostrophes with exponents of one or eleven. Though the primes notation is more shorthand and quicker to write, so many people prefer it.