Final answer:
To find ∂z/∂s and ∂z/∂t using the chain rule, substitute the given equations into z, then differentiate z with respect to s and t using the chain rule.
Step-by-step explanation:
To find ∂z/∂s and ∂z/∂t using the chain rule, we need to express z in terms of s and t. Given z = e^(x + 2y) and the equations x = s/t and y = t/s, we can substitute these equations into z to get z = e^((s/t) + 2(t/s)).
Next, we can differentiate z with respect to s to find ∂z/∂s by treating t as a constant. Using the chain rule, we get ∂z/∂s = (2/t)e^((s/t) + 2(t/s)).
To find ∂z/∂t, we differentiate z with respect to t, treating s as a constant. Applying the chain rule, we find ∂z/∂t = (-1/t^2)e^((s/t) + 2(t/s)).