DF _ _ _ _ _ _ _ _ _ _ _ _ operator

The df operator finds partial derivatives with respect to one or more variables.

syntax:

<expression> can be any valid REDUCE algebraic expression. <var> must be a kernel, and is the differentiation variable. <number> must be a non-negative integer.

examples:

df(x**2,x); 

  2*X 



df(x**2*y + sin(y),y); 

            2
  COS(Y) + X  



df((x+y)**10,z); 

  0 




df(1/x**2,x,2); 

  6
  ---
   4
  X



df(x**4*y + sin(y),y,x,3); 

  24*X 



for all x let df(tan(x),x) = sec(x)**2; 


df(tan(3*x),x); 

            2
  3*SEC(3*X)

An error message results if a non-kernel is entered as a different iation operator. If the optional number is omitted, it is assumed to be 1. See the declaration depend to establish dependencies for implicit differentiation.

You can define your own differentiation rules, expanding REDUCE's capabilities, using the let command as shown in the last example above. Note that once you add your own rule for differentiating a function, it supersedes REDUCE's normal handling of that function for the duration of the REDUCE session. If you clear the rule ( clearrules), you don't get back to the previous rule.