Function: diff (<expr>, <x_1>, <n_1>, ..., <x_m>, <n_m>)
Function: diff (<expr>, <x>, <n>)
Function: diff (<expr>, <x>)
Function: 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.
true, derivatives are displayed as subscripts. Otherwise, derivatives are displayed in the Leibniz notation,
(%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, ... to be used. If
coordinates has not been assigned a value, then the variables will be treated as in (1) above.
There are also some inexact matches for
?? diff to see them.
(%o1) true (%i2)