Question

Use the chain rule calculate dw/dr , dw/ds and dw/dt

W=in(x+2y+3z) , x=r^2 + t^2 , y =s^2 - t^2 , z=r^2 + s^2

Answer 1

,
,

Explanation:

We proceed to derive each expression by rule of chain. Let be
,
,
and
:

(1)

(2)

(3)