Maxima 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