Maxima Function
diff (expr, x_1, n_1, ..., x_m, n_m)
diff(expr,x,n)
diff(expr,x)
diff(expr)
Returns the derivative or differential of expr with respect to some or all variables in expr.
diff (expr, x, n)
returns the n'th derivative of expr
with respect to x.
diff (expr, x_1, n_1, ..., x_m, n_m)
returns the mixed partial derivative of expr with respect to x_1, ..., x_m.
It is equivalent to diff (... (diff (expr, x_m, n_m) ...), x_1, n_1)
.
diff (expr, x)
returns the first derivative of expr with respect to
the variable x.
diff (expr)
returns the total differential of expr,
that is, the sum of the derivatives of expr with respect to each its variables
times the differential del
of each variable.
No further simplification of del
is offered.
The noun form of diff
is required in some contexts,
such as stating a differential equation.
In these cases, diff
may be quoted (as 'diff
) to yield the noun form
instead of carrying out the differentiation.
When derivabbrev
is true
, derivatives are displayed as subscripts.
Otherwise, derivatives are displayed in the Leibniz notation, dy/dx
.
Examples:
(%i1) diff (exp (f(x)), x, 2); 2 f(x) d f(x) d 2 (%o1) %e (--- (f(x))) + %e (-- (f(x))) 2 dx dx (%i2) derivabbrev: true$ (%i3) 'integrate (f(x, y), y, g(x), h(x)); h(x) / [ (%o3) I f(x, y) dy ] / g(x) (%i4) diff (%, x); h(x) / [ (%o4) I f(x, y) dy + f(x, h(x)) h(x) - f(x, g(x)) g(x) ] x x x / g(x)
For the tensor package, the following modifications have been incorporated:
(1) The derivatives of any indexed objects in expr will have the variables x_i appended as additional arguments. Then all the derivative indices will be sorted.
(2) The x_i may be integers from 1 up to the value of the variable
dimension
[default value: 4]. This will cause the differentiation to
be carried out with respect to the x_i'th member of the list coordinates
which
should be set to a list of the names of the coordinates, e.g.,
[x, y, z, t]
. If coordinates
is bound to an atomic variable, then that
variable subscripted by x_i will be used for the variable of
differentiation. This permits an array of coordinate names or
subscripted names like X[1]
, X[2]
, ... to be used. If coordinates
has
not been assigned a value, then the variables will be treated as in (1)
above.