Does anyone have any tips for using Sage to take derivatives of functions of many variables?
For example, if I define
w(x,y) = x^2 + y^2 (say)
and then if I suppose that x and y depend on an independent variable t, the chain rule applies for finding w.diff(t). The only way I found to do this in Sage is
var('t')
x(t) = cos(t) (say)
y(t) = sin(t)
w(x,y) = x^2 + y^2
w.diff(t)
But this isn't really using the chain rule. If I instead try
var('x,y')
(define w again)
(define x and y again)
w.diff(t)
Out: (x,y) |--> 0
Apparently it thinks the derivative is zero because it still thinks x and y are two independent variables where they appear in w, even though you get
x
Out: t |--> cos(t)
and similarly for y. Any suggestions? Thanks.
