Notation for the Second Derivative
Key Questions
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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.
Jacob F.
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Aug 1 2014
Questions
Graphing with the Second Derivative
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Relationship between First and Second Derivatives of a Function
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Analyzing Concavity of a Function
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Notation for the Second Derivative
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Determining Points of Inflection for a Function
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First Derivative Test vs Second Derivative Test for Local Extrema
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The special case of x⁴
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Critical Points of Inflection
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Application of the Second Derivative (Acceleration)
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Examples of Curve Sketching