• incanter

# deriv*

## incanter.symbolic

• (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 incanter/symbolic.clj:74 top

```(defn deriv*
"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)

"
([exp v]
(cond
(number? exp) 0
(same-var? exp v) 1
(and (same-var? exp) (not= exp v)) 0
(sum? exp) (make-sum (deriv* (second exp) v) (deriv* (reduce-expr exp '+) v))
(difference? exp) (make-sum (deriv* (second exp) v)
(deriv* (make-prod -1 (reduce-expr exp '+)) v))
(product? exp)
(make-sum
(make-prod (second exp)
(deriv* (reduce-expr exp '*) v))
(make-prod (deriv* (second exp) v)
(reduce-expr exp '*)))
(quotient? exp) (deriv* (conv-qtnt exp) v)
(expnt? exp)
(let [u (second exp)
n (expnt exp)]
(make-prod (make-prod
(expnt exp)
(make-expnt (second exp) (make-sum (expnt exp) -1)))
(deriv* (second exp) v)))
(chainable? exp)
(let [u (first exp)
n (second exp)]
(cond
(number? n) 0;things could be out-of-bounds a la log(0), but that's philosophical
(= 'sin u) (make-prod (list 'cos n) (deriv* n v))
(= 'cos u) (make-prod (list '* -1 (list 'sin n)) (deriv* n v))
(= 'tan u) (make-prod (list 'pow (list 'cos n) -2) (deriv* n v))
;multiply by inverse of denominator is same as numerator/denominator
(= 'log u) (make-prod (deriv* n v) (list 'pow n -1))
(= 'exp u) (make-prod (list 'exp n) (deriv* n v))
true false));should not happen as chainable? refers to a list that
;we should completely specify here
true (list 'deriv* exp v);some kind of error here, return a description of
;"the derivative of this function" rather than the actual result
))
([exp vr degree]
(loop [x exp v vr dgr degree]
(if (zero? dgr) x
(recur (deriv* x v) v (dec dgr) )))))```
Vars in incanter.symbolic/deriv*: * + = and cond dec defn let list loop not= number? second zero?
Used in 0 other vars