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ratdiff

Maxima Function

Calling Sequence

ratdiff (expr, x)

Description

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.

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
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