The Maxima on-line user's manual

Algebra 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>.

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) ```

Related Examples

ratdiff

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

ratdiff (expr, x);

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

Calculate

? ratdiff;

Calculate

ratdiff

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

ratdiff (expr, x);

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

Calculate

? ratdiff;

Calculate