# help on using chain rule in Sage

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.