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326 Functions and commands
Calculus
Differentiate With one expression as argument, returns derivative of the
expression with respect to x. With one expression and one
variable as arguments, returns the derivative or partial
derivative of the expression with respect to the variable. With
one expression and more than one variable as arguments,
returns the derivative of the expression with respect to the
variables in the second argument. These arguments can be
followed by $k (k is an integer) to indicate the number of times
the expression should be derived with respect to the variable.
For example, diff(exp(x*y),x$3,y$2,z) is the same as
diff(exp(x*y),x,x,x,y,y,z).
diff(Expr,[var])
or
diff(Expr,var1$k1,var2$k2,...)
Example:
diff(x^3-x) gives 3*x^2-1
Integrate Returns the indefinite integral of an expression. With one
expression as argument, returns the indefinite integral with
respect to x. With the optional second, third and fourth
arguments you can specify the variable of integration and the
bounds of the integrate.
int(Expr,[Var(x)],[Real(a)],[Real(b)])
Example:
int(1/x) gives ln(abs(x))
Limit Returns the limit of an expression when the variable
approaches a limit point a or +/– infinity. With the optional
fourth argument you can specify whether it is the limit from
below, above or bidirectional (–1 for limit from below, +1 for
limit from above, and 0 for bidirectional limit). If the fourth
argument is not provided, the limit returned is bidirectional.
limit(Expr,Var,Val,[Dir(1, 0, -1)])
Example:
limit((n*tan(x)-tan(n*x))/(sin(n*x)-
n*sin(x)),x,0)
gives 2