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How does Leibniz notation work for second derivatives?

Answer 1

Christopher Allers

The Leibniz notation for #y''# is #{d^2y}/{dx^2}#.

For example, if #y=sinx#, then #{dy}/{dx}=d/{dx}(sinx)=cosx# and #{d^2y}/{dx^2}=d/dx(cosx)=-sinx#.

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Answer 2

Luke Alvarez

Leibniz notation for second derivatives involves using prime notation.

For a function (y = f(x)), the first derivative is denoted as (y' = f'(x)) or (dy/dx).

The second derivative is denoted as (y'' = f''(x)) or ((d^2y)/(dx^2)).

Alternatively, Leibniz notation can be extended by adding primes for each derivative, such as (y''') for the third derivative and so on.

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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.