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The DIFFERENTIATE function returns the derivative determined from two columns of tabular data in a  Lookup Table or a Lookup file


DIFFERENTIATE('Table Name','ColName1','ColName2',ColName2=Value, FirstRow, LastRow)


'Table Name' is a string constant or string variable  that provides the name of the Lookup table in the Lookup Window or the name of an existing Lookup file stored on disk. The string constant must be enclosed within single quote marks.  Lookup table names appear on the tabs at the top of the Lookup Table Window.   If the name of a disk file is supplied, it must be the name of an existing Lookup file having either the binary or ASCII Lookup file Format.  ColName1 and ColName2 are the column header names.  These variables must be either be string constants or string variables.  Since there is no ambiguity, the single quotes for string constants are optional.


The next parameter is of the form ColName2=Value where the text to the left of the equal sign can be either of the column header names (ColName1 or ColName2) specified with the two previous parameters.  Note that if a string variable was provided for the column name, then the same string variable must be used for this parameter.  Value is a numerical value or expression.   EES will return an estimate of the derivative  d(ColName1)/ d(ColName2) at a point fixed by the specified value of either ColName1 or ColName2.


FirstRow and LastRow are optional.  If they are not provided, the Differentiate function will use all of the rows in the table.  If FirstRow and LastRow are provided, only the specified range of rows will be used.  If LastRow is set to 0 or a number greater than then number of rows in the table, the Differentiate function will set it to the number of rows in the table.


The DIFFERENTIATE command will use cubic interpolation between points to determine the estimate of the derivative if there are at least five rows in the table or file are needed to use this command.  If there are less than 5, linear interpolation will be used.  


Note:  use a semicolon instead of a comma as the list separator when using the European numerical format)


Note that the data in the specified columns of the table must be monotonic, i.e., increasing or decreasing.  The Differentiate function will fail to find a correct result if this is not the case.  


Open file Copper.EES in the EES\Userlib\Examples folder for an example demonstrating the use of this function.


See also:  DIFFERENTIATE1, DIFFERENTIATE2, Mathematical Functions