Question

Use the Chain Rule to find∂z/∂s and∂z/∂t. (Enter your answer only in termsof s and t.)

z = ex + 7y, x = s/t, y = t/s
∂z/∂s =
∂z/∂t =

Answer 1

To find ∂z/∂s and ∂z/∂t using the Chain Rule, substitute the expressions for x and y into the equation for z and differentiate z with respect to s and t separately.

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 and differentiate it with respect to each variable separately. We are given that z = ex + 7y, x = s/t, and y = t/s.

First, we substitute the expressions for x and y into the equation for z:

z = e(s/t) + 7(t/s).

Next, we differentiate z with respect to s and t:

∂z/∂s = e(s/t)(1/t) - 7(t/s²).

∂z/∂t = e(s/t)(-s/t²) + 7(1/s).