Solving a Partial Derivative Problem with Substitution

[Derill03]

Find par(z)/par(t) at s=1, t=0
when z= ln(x+y), x=s+t, y=s-t

Not sure how to approach cause if i plug in s's and t's i get an answer of 0 because taking the partial with respect to t yields a zero. Can someone shed some light on how to correctly solve?

par(z)/par(t) = partial derivative of z with respect to t

 

[djeitnstine]

find $$\frac{\partial{z}}{\partial{x}} \frac{\partial{x}}{\partial{t}}}$$ and $$\frac{\partial{z}}{\partial{y}} \frac{\partial{y}}{\partial{t}}$$

 

[HallsofIvy]

The chain rule for partial derivatives is
$$\frac{\partial z}{\partial t}= \frac{\partial z}{\partial x}\frac{\partial x}{\partial t}+ \frac{\partial z}{\partial y}\frac{\partial y}{\partial t}$$

 

[Derill03]

I just don't know how to deal with it in the form its in. The s and t are what are confusing me, can u give me some sort of an example?

The way i did it is substitute s and t for y and x so i get ln(2s) but when u take partial with respect to t you get 0? is this correct?