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 u D: n  mu mu Secant Slope

 x u D: 1 y is the secant slope of the function u through the points y and y+x . The secant slope is generalized to the case x u D. n y in the manner of the derivative D. . The argument x may be a list, giving several slopes. In the general case, each item of x has the shape {. \$\$"r y, where r is the rank of u, therefore specifying the increment in each possible direction. An argument x of lower rank is extended in the usual manner. For example, x=: 1e_8 provides the same increment in each direction and, because of the small magnitude, yields an approximation to the derivative.

```   log=: ^.
y=: 2 3 4
1 log D:1 y
0.405465 0.287682 0.223144

incr=: 1 0.1 0.01 1e_8
incr log D:1/y
0.405465 0.287682 0.223144
0.487902 0.327898 0.246926
0.498754 0.332779 0.249688
0.5 0.333333     0.25

log D.1 y
0.5 0.333333 0.25
%y
0.5 0.333333 0.25

f=: +/@:*:"1
g=: +/@:*:\"1
(f y) ; (1 f D:1 y) ; (1 0.1 1e_8 f D:1 y)
+--+-----+--------------+
|29|5 7 9|  5  0.61 8e_8|
|  |     | 50   6.1 8e_7|
|  |     |5e8 6.1e7    8|
+--+-----+--------------+

(g y) ; (1 g D:1 y)
+-------+-----+
|4 13 29|5 0 0|
|       |5 7 0|
|       |5 7 9|
+-------+-----+

```

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