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The difference quotient is sometimes also called the Newton quotient [10] [12] [13] [14] (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat). [ 15 ] Overview
The symmetric difference quotient is employed as the method of approximating the derivative in a number of calculators, including TI-82, TI-83, TI-84, TI-85, all of which use this method with h = 0.001. [2] [3]
2.4 Quotient rule for division by a scalar. 2.5 Chain rule. 2.6 Dot product rule. 2.7 Cross product rule. 3 Second derivative identities. ... 4.2.1 Surface–volume ...
On T 2 it is known that if f is in H k, then the difference quotient δ h f = h −1 (R h f − f ) → ∂ y f in H k−1; if the difference quotients are bounded in H k then ∂ y f lies in H k. Both assertions are consequences of the formula:
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For differentiable functions, the symmetric difference quotient does provide a better numerical approximation of the derivative than the usual difference quotient. [3] The symmetric derivative at a given point equals the arithmetic mean of the left and right derivatives at that point, if the latter two both exist. [1] [2]: 6
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