# API for symbolic - Incanter1.5.5 (stable)

by Bryce Nyeggen, with modifications by David Edgar Liebke

Full namespace name: incanter.symbolic

## Overview

`A library for performing symbolic math, a port from SICP (http://mitpress.mit.edu/sicp/).`

## deriv

macro
```Usage: (deriv exp v)
(deriv exp v degree)
```
```Macro for symbolic differentiation. with 2 args, takes 1st degree deriv.
with 3, takes arbitrary degrees. contains all deriv rules for basic funcs.

Examples:

(use '(incanter core symbolic))

(deriv (+ x 3) x) ; => 1
(deriv (* x y) x) ; => y
(deriv (* (* x y) (+ x 3)) x) ; => (+ (* (+ x 3) y) (* x y))
(deriv (* (* x y) (+ x 3)) y) ; => (* (+ x 3) x)

(deriv (* x y (+ x 3)) x) ; => (+ (* y (+ x 3)) (* y x))
(deriv (* x y (+ x 3)) y) ; => (* (+ x 3) x)

(deriv (sin x) x) ; => (cos x)
(deriv (cos x) x) ; => (* -1 (sin x))

(deriv (sin (* x y)) y) ; => (* x (cos (* x y)))

(deriv (pow x 3) x) ; => (* 3 (pow x 2))
(deriv (** x 3) x) ; => (* 3 (pow x 2))

(deriv (pow x 3) x 2) ; => (* 3 (* 2 x))

(deriv (* x y (+ x 3)) x 2) ; => (+ y y)
(deriv (* x y (+ x 3)) x 3) ; => 0

(deriv (+ (* 3 x) (* 8 x)) x) ; => 11

;; NOT WORKING YET

(deriv (/ 1 x) x) ; => (* (deriv* (* (x)) x) (* -1 (pow (* (x)) -2)))
^-- need to fix```

Source

## deriv*

function
```Usage: (deriv* exp v)
(deriv* exp vr degree)
```
```Main sub-function for differentiation. with 2 args, takes 1st degree deriv.
with 3, takes arbitrary degrees. contains all deriv rules for basic funcs.

Examples:

(use '(incanter core symbolic))

(deriv* '(+ x 3) 'x)
(deriv* '(* x y) 'x)
(deriv* '(* (* x y) '(+ x 3)) x)
(deriv* '(* (* x y) (+ x 3)) 'y)

(deriv* '(* x y (+ x 3)) 'x)
(deriv* '(* x y (+ x 3)) 'y)

(deriv* '(* x y (+ x 3)) 'x 2)
(deriv* '(* x y (+ x 3)) 'x 3)
```

Source

## deriv-fn

macro
```Usage: (deriv-fn [& args] expr v)
(deriv-fn [& args] expr v degree)
```
```Examples:
(use '(incanter core symbolic))

(deriv-fn [x y] (+ (* x y) x) x)

((deriv-fn [x y] (+ (* x y) x) x) 5 9)

(use 'incanter.charts)
(doto (function-plot sin -5 5)
(add-function (deriv-fn [x] (sin x) x) -5 5)
(add-function (deriv-fn [x] (sin x) x 2) -5 5)
view)

(let [f (fn [x] (pow x 2))
df (deriv-fn [x] (pow x 2) x)]
(doto (function-plot f -5 5)
view))

(let [f (fn [x] (pow x 3))
df (deriv-fn [x] (pow x 3) x)]
(doto (function-plot f -5 5)
view))

;; NOT WORKING YET

(let [f (fn [x] (/ 1 x ))
df (deriv-fn [x] (/ 1 x) x)]
(doto (function-plot f 0.5 5)
view))
```

Source

## deriv-fn*

function
```Usage: (deriv-fn* [& args] expr v)
(deriv-fn* [& args] expr v degree)
```
```Examples:
(use '(incanter core symbolic))

(deriv-fn* '[x y] '(+ (* x y) x) 'x)

((deriv-fn* '[x y] '(+ (* x y) x) 'x) 5 9)
```

Source

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