Kollokvium0307/Носов Иван/README.md

Дифференцирование

Ссылка на видеоразбор

https://youtu.be/Kh0shn9UW6Y

Код из книги

#let rec differentiate x tm = match tm with
Var y -> if y = x then Const "1" else Const "0"
| Const c -> Const "0"
| Fn("-",[t]) -> Fn("-",[differentiate x t])
| Fn("+",[t1;t2]) -> Fn("+",[differentiate x t1;
differentiate x t2])
| Fn("-",[t1;t2]) -> Fn("-",[differentiate x t1;
differentiate x t2])
|    Fn("*",[t1;t2]) ->
Fn("+",[Fn("*",[differentiate x t1; t2]);
Fn("*",[t1; differentiate x t2])])
| Fn("inv",[t]) -> chain x t
(Fn("-",[Fn("inv",[Fn("^",[t;Const "2"])])]))
| Fn("^",[t;n]) -> chain x t
(Fn("*",[n; Fn("^",[t; Fn("-",[n; Const "1"])])]))
| Fn("exp",[t]) -> chain x t tm
| Fn("ln",[t]) -> chain x t (Fn("inv",[t]))
| Fn("sin",[t]) -> chain x t (Fn("cos",[t]))
| Fn("cos",[t]) -> chain x t
(Fn("-",[Fn("sin",[t])]))
| Fn("/",[t1;t2]) -> differentiate x
(Fn("*",[t1; Fn("inv",[t2])]))
| Fn("tan",[t]) -> differentiate x
(Fn("/",[Fn("sin",[t]); Fn("cos",[t])]))
and chain x t u = Fn("*",[differentiate x t; u]);;