Analytical differentiation

Some ArtSGraph functions take expression as argument and returns expression as its value. Function diff(F,x), which performs analytical differentiation, is one of them.

 

Function  diff(F,x) obtains derivative of expression F with respect to variable x.  

Example

f=sin(x)/ln(x)                    

d=diff(f,x)                    ; d is  (ln(x)*cos(x)-sin(x)/x)/(ln(x))2

 

 

Expression F can contain other variables besides x.  In this case diff(F,x) returns partial derivative.

Example

f=a*sin(x)

d1=diff(f,x)                  ; d1 is a*cos(x)

d2=diff(f,a)                  ; d2 is sin(x)

d3=diff(f,y)                  ; d3 is 0

 

Using diff(F,x) you can calculate derivatives of high orders.

Example

F=sin(x)*cos(y)

Fxx=diff(diff(f,x),x)                ; Fxx is   cos(y)*(-sin(x))

Fyy=diff(diff(f,y),y)                ; Fyy is   sin(x)*(-cos(y))

Fxy=diff(diff(f,x),y)                ; Fxy is   cos(x)*(-sin(y))

Fyx=diff(diff(f,y),x)                ; Fyx is   (-sin(y))*cos(x)