The operator in brackets ( in the final expression ) is also called the total derivative operator ( with respect to " t " ).
22.
If we write " f " using coordinate functions, so that, then the total derivative can be expressed using the partial derivatives as a matrix.
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And the total derivative of pressure with respect to temperature may be integrating from an initial phase \ alpha to a final phase \ beta, to obtain
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That is, if " f " is a real-valued function of a real variable, then the total derivative exists if and only if the usual derivative exists.
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Financial companies accounted for 98 percent, or $ 18.6 trillion, of the total derivatives among the 371 companies that reported information on their activities, according to the study.
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In mathematics, a "'partial derivative "'of a with the others held constant ( as opposed to the total derivative, in which all variables are allowed to vary ).
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Substituting the above equation into the total derivative of the Gibbs energy equation and by utilizing the result is equated to the non-pressure volume work when surface energy is considered:
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Financial companies accounted for 98 percent, or $ 18 . 6 trillion, of the total derivatives among the 371 companies that reported information on their activities, according to the study.
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This way we get a new ideal " I " of \ mathcal { F } ( \ pi ) which is now closed under the operation of taking total derivative.
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The time derivatives of the generalized coordinates are called the generalized velocities, and for each particle the transformation of its velocity vector, the total derivative of its position with respect to time, is
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