4.1 Differential Operator ¶

Operator: differential expr ¶

Operator: ' expr ¶

The Jacal command differential computes the derivative of the expression expr with respect to a generic derivation. It is generic in the sense that nothing is assumed about its effect on the individual variables. The derivation is denoted by a right quote.

(%0061) differential(x^2+y^3);
                   2
%0061: 2 x x' + 3 y  y'
(%0062) (x^2+y^3)';
                   2
%0062: 2 x x' + 3 y  y'

4.2 Derivatives ¶

Command: diff expr var1 … ¶

The Jacal command diff computes the derivative of the expression expr with respect to var1, ….

(%0063) diff(x^2+y^3,y);
          2
%0063: 3 y

Command: partial expr var1 … ¶

The Jacal command partial computes the partial derivative of the expression expr with respect to var1, ….

(%0064) partial(x^2+@1^3,1);
           2
%0064: 3 @1

4.3 Integration ¶

Command: integrate expr var ¶

Returns the indefinite integral of rational expression expr, if that integral is a rational expression containing at most one radical involving var.

(%0065) integrate((3+x^2)*(1+x^2)^(2/3)/(3+6*x^2+3*x^4),x);
               2 2/3
       x (1 + x )
%0065: -------------
               2
          1 + x
(%0066) integrate((1+x^2)^(2/3),x);

;;; could-not-find-algebraic-anti-derivative
 non-decreasing-rxd 2 vs 0
(%0066) integrate(x*(1+x^2)^(2/3),x);
               2        2 2/3
       (3 + 3 x ) (1 + x )
%0066: ----------------------
                 10

Command: integrate expr var a b ¶

If the indefinite integral of rational expression expr is a rational expression (optionally including a radical involving var), then integrate returns the difference of that integral evaluated at b and a.

(%0067) integrate(x*(1+x^2)^(2/3),x,0,1);
               2/3
       -3 + 6 2
%0067: -----------
           10