What is notation for the Second Derivative?

1 Answer
Aug 1, 2014

If you prefer Leibniz notation, second derivative is denoted #(d^2y)/(dx^2)#.

Example:

#y = x^2#

#dy/dx = 2x#

#(d^2y)/(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' = 2x#
#y'' = 2#

Similarly, if the function is in function notation:

#f(x) = x^2#
#f'(x) = 2x#
#f''(x) = 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.