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 Polynomial Derivative p..  1 0 1 Polynomial Integral

 Applied to a polynomial (coefficients or boxed roots), p.. produces the coefficients of the derivative of polynomial. For example: ``` p.. 1 2 3 4 5 2 6 12 20 p.. 5 4 3 2 1 4 6 6 4 p.. 2; 1j1 1j_1 _4 4 p.. p. 2; 1j1 1j_1 _4 4 ``` x p.. y produces the integral of polynomial y with a constant term of x . Thus: ``` 5 p.. 4 6 6 4 5 4 3 2 1 1 p.. 2 6 12 20 1 2 3 4 5 ```

Further examples:
```   p.. 1&o. t. i. 11x              NB. derivative of sine
1 0 _1r2 0 1r24 0 _1r720 0 1r40320 0
2&o. t. i.10x                   NB. cosine
1 0 _1r2 0 1r24 0 _1r720 0 1r40320 0

p.. 2&o. t. i. 11x              NB. derivative of cosine
0 _1 0 1r6 0 _1r120 0 1r5040 0 _1r362880
-@(1&o.) t. i.10x               NB. minus sine
0 _1 0 1r6 0 _1r120 0 1r5040 0 _1r362880
- (1&o. t. i.10x)
0 _1 0 1r6 0 _1r120 0 1r5040 0 _1r362880

p..^:(i.@#) 8 \$ 1
1    1    1   1   1  1 1 1
1    2    3   4   5  6 7 0
2    6   12  20  30 42 0 0
6   24   60 120 210  0 0 0
24  120  360 840   0  0 0 0
120  720 2520   0   0  0 0 0
720 5040    0   0   0  0 0 0
5040    0    0   0   0  0 0 0
```

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