Chain Rule: compute dw/ds, dw/dt at (-5, 1), w=-5xy+5yz-xz

[think.ms.tink]

Let
w=-5xy+5yz-xz
x=st
y=e^st
z=t^2
Compute dw/ds @ (-5,1) and dw/dt @ (-5,1).

so far i have take the derivative of w to be
x=-5y-z
y=-5x+5y
z=5y-x
and dx/ds=t, dy/ds=te^st, dz/ds=t^2
and dx/dt=s, dy/dt=se^st, dz/dt=2t
Are my derivations correct and what happens next? Thanks.

 

[Deleted member 4993]

Let
w=-5xy+5yz-xz
x=st
y=e^st
z=t^2
Compute dw/ds @ (-5,1) and dw/dt @ (-5,1).

so far i have take the derivative of w to be
x=-5y-z
y=-5x+5y
z=5y-x
and dx/ds=t, dy/ds=te^st, dz/ds=t^2
and dx/dt=s, dy/dt=se^st, dz/dt=2t
Are my derivations correct and what happens next? Thanks.

What is the expression for ?w?

?w = (dw/dx) dx + (dw/dy) dy + (dw/dz) dz

then

dw/ds = (dw/dx) (dx/ds) + (dw/dy) (dy/ds) + (dw/dz) (dz/ds)

Then continue ....