u d. n y Ordinary Derivative Conjunction
The ordinary n-th derivative of [the mathematical function implemented by] verb u.
^. d. 1 NB. derivative of ln(x) is 1/x % ^.@(1&o.) d. 1 NB. derivative of ln(sin x) is cos x * 1/sin x 2&o. * %@(1&o.) (^&2 + ^&3) d. 1 NB. 1st derivative of x^2 + x^3 0 2 3x&p. (^&2 + ^&3) d. 2 NB. 2nd derivative of x^2 + x^3 2 6x&p.
Derivative (u D. n)
2. u must be one of the verbs, or combinations of verbs, for which J knows the derivative. These are:
Allowable forms of u in u d. 1 Type Allowed Values constants _9: through 9: _: m"0 monads <: >: +: *: - -. -: % %: ^ ^. [ ] j. o. r. bonded dyads m&+ m&* m&- m&% m&%: m&^ m&^. m&! m&p. +&n *&n -&n %&n ^&n ^.&n circle functions 0&o. (-.&.*:), 1&o. (sin), 2&o. (cos), 3&o. (tan), 5&o. (sinh), 6&o. (cosh), 7&o. (tanh) inverses of the above for all monads; for bonded dyads except m&! m&p. ^.&n; for no circle functions other inverses m&j.^:_1 m&r.^:_1 %:&n^:_1 j.&n^:_1 r.&n^:_1 compounds where
u and v are allowed
u@v u@:v u&v u&:v (u + v) (u * v) (u - v) (u % v) (u , v) rank "n allowed and ignored
3. n may be negative to calculate the nth antiderivative (with the constant of integration equal to 0). The allowed forms of u are the same as for u d. 1 , except that m&%: m&^. ^.&n m&^^:_1 %:&n^:_1 (u * u) (u % u) (u , u) are not allowed.
4. u d. n integrates symbolically rather than numerically, and should be used rather than Derivative (D.) where possible.
1. n may be a list, in which case the result for each atom of y will be the list of derivatives of orders n.