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What is notation for the Second Derivative?

Answer 1

William Abdalla

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.

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Answer 2

Isabella Ackerman

The notation for the second derivative of a function ( f(x) ) is ( f''(x) ) or ( \frac{d^2}{dx^2}f(x) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.