Maxima Function
gradef (f(x_1, ..., x_n), g_1, ..., g_m)
gradef(a,x,expr)
Defines the partial derivatives (i.e., the components of the gradient) of the function f or variable a.
gradef (f(x_1, ..., x_n), g_1, ..., g_m)
defines df/dx_i as g_i,
where g_i is an expression; g_i may be a function call, but not the name of a function.
The number of partial derivatives m may be less than the number of arguments n,
in which case derivatives are defined with respect to x_1 through x_m only.
gradef (a, x, expr) defines the derivative of variable a
with respect to x as expr.
This also establishes the dependence of a on x (via depends (a, x)).
The first argument f(x_1, ..., x_n) or a is quoted,
but the remaining arguments g_1, ..., g_m are evaluated.
gradef returns the function or variable for which the partial derivatives are defined.
gradef can redefine the derivatives of Maxima's built-in functions.
For example, gradef (sin(x), sqrt (1 - sin(x)^2)) redefines the derivative of sin.
gradef cannot define partial derivatives for a subscripted function.
printprops ([f_1, ..., f_n], gradef) displays the partial derivatives
of the functions f_1, ..., f_n, as defined by gradef.
printprops ([a_n, ..., a_n], atomgrad) displays the partial derivatives
of the variables a_n, ..., a_n, as defined by gradef.
gradefs is the list of the functions
for which partial derivatives have been defined by gradef.
gradefs does not include any variables
for which partial derivatives have been defined by gradef.
Gradients are needed when, for example, a function is not known explicitly but its first derivatives are and it is desired to obtain higher order derivatives.