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The Maxima on-line user's manual

Algebra Calculator

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Ratdiff Calculator

Ratdiff

Function: ratdiff (<expr>, <x>) Differentiates the rational expression <expr> with respect to <x>. <expr> must be a ratio of polynomials or a polynomial in <x>. The argument <x> may be a variable or a subexpression of <expr>.

expr: (4*x^3 + 10*x - 11)/(x^5 + 5);
 ratdiff (expr, x);
 expr: f(x)^3 - f(x)^2 + 7;
 ratdiff (expr, f(x));
 expr: (a + b)^3 + (a + b)^2;
 ratdiff (expr, a + b);

The result is equivalent to diff, although perhaps in a different form. ratdiff may be faster than diff, for rational expressions.

ratdiff returns a canonical rational expression (CRE) if expr is a CRE. Otherwise, ratdiff returns a general expression.

ratdiff considers only the dependence of <expr> on <x>, and ignores any dependencies established by depends.

Example:

          (%i1) expr: (4*x^3 + 10*x - 11)/(x^5 + 5);
                                     3
                                  4 x  + 10 x - 11
          (%o1)                   ----------------
                                        5
                                       x  + 5
          (%i2) ratdiff (expr, x);
                              7       5       4       2
                           8 x  + 40 x  - 55 x  - 60 x  - 50
          (%o2)          - ---------------------------------
                                    10       5
                                   x   + 10 x  + 25
          (%i3) expr: f(x)^3 - f(x)^2 + 7;
                                   3       2
          (%o3)                   f (x) - f (x) + 7
          (%i4) ratdiff (expr, f(x));
                                     2
          (%o4)                   3 f (x) - 2 f(x)
          (%i5) expr: (a + b)^3 + (a + b)^2;
                                        3          2
          (%o5)                  (b + a)  + (b + a)
          (%i6) ratdiff (expr, a + b);
                              2                    2
          (%o6)            3 b  + (6 a + 2) b + 3 a  + 2 a

(%o1)                                true
(%i2) 

Ratdiff Example

Related Examples

ratdiff

expr: (4*x^3 + 10*x -...

ratdiff (expr, x);

expr: f(x)^3 - f(x)^...

Calculate

ratdiff

expr: (4*x^3 + 10*x -...

ratdiff (expr, x);

expr: f(x)^3 - f(x)^...

Calculate