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## Plotting Derivatives by Joining a Table with Itself

By joining a table onto itself, you can look at expressions of values from the same column but different records. For example, suppose you want to plot the derivative of column  NE where you have NE as a function of RADIUS and TIME, and TIME is evenly spaced with an increment of 0.01 seconds. You would join this table with itself, such that the rows are offset. To do this, first go back to the top menu (`\0`) and select two copies of the table: PT GP8840 GP8840;. Then select the JOIN option and define the join as (A.TIME-0.01=B.TIME)AND(A.RADIUS=B.RADIUS). Now for the y axis, you can specify (A.NE-B.NE)/(A.TIME-B.TIME) as in Figure 7.

```    \* Options are:
1) Y < (A.NE-B.NE)/(A.TIME-B.TIME) >
2) X < TIME >
3) Constraints < RADIUS=70 (TIME>2.8)AND(TIME<3.4) >
4) Symbols < >
5) Graph ranges  <Y:0.00E+00,0.00E+00,LIN><X:0.00E+00,0.00E+00,LIN>
6) G+ Graph Plus <Auto-scale_Y:min=T,max=T><Auto-scale_X:min=T,max=T>
7) Key for dynamic cursor option <A.NE>
8) Join   <(A.TIME-0.01=B.TIME)AND(A.RADIUS=B.RADIUS)>
...```
A join of (A.TIME-0.02=B.TIME)AND(A.RADIUS=B.RADIUS), i.e., over two records, would result in a smoother derivative. By defining (A.NE-B.NE)/(A.TIME-B.TIME) as DNEDT in an expression table, you can succintly use the derivative in other expressions.

Figure 7: Plot a derivative by joining a table with itself

Marilee Thompson
Fri Jul 11 17:05:56 EDT 1997