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Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The symbol () is the derivative of the temperature T with respect to the volume V while keeping constant the entropy (subscript) S, while () is the derivative of the temperature with respect to the volume while keeping constant the pressure P. This becomes necessary in situations where the number of variables exceeds the degrees of freedom, so ...
Further time derivatives have also been named, as snap or jounce (fourth derivative), crackle (fifth derivative), and pop (sixth derivative). [12] [13] The seventh derivative is known as "Bang," as it is a logical continuation to the cycle. The eighth derivative has been referred to as "Boom," and the 9th is known as "Crash."
Another less serious suggestion is snap (symbol s), crackle (symbol c) and pop (symbol p) for the 4th, 5th and 6th derivatives respectively. Higher derivatives do not yet have names because they do not come up very often.
Here ∂ is a rounded d called the partial derivative symbol. To distinguish it from the letter d, ∂ is sometimes pronounced "der", "del", ...
In two dimensions, the Levi-Civita symbol is defined by: = {+ (,) = (,) (,) = (,) = The values can be arranged into a 2 × 2 antisymmetric matrix: = (). Use of the two-dimensional symbol is common in condensed matter, and in certain specialized high-energy topics like supersymmetry [1] and twistor theory, [2] where it appears in the context of 2-spinors.
The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic , but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form
The most common differential operator is the action of taking the derivative. Common notations for taking the first derivative with respect to a variable x include: , , , and . When taking higher, nth order derivatives, the operator may be written: