Answer:
dz / dt = -50
Step-by-step explanation:
To solve the chain rule must apply, we have all the necessary values to make the calculation, as follows:
using the chain rule, we find:
dz / dt = (∂z / ∂x) * (∂x / ∂t) + (∂z / ∂y) * (∂y / ∂t)
Evaluating when t = 9, we have to:
fx (6, 4) * g '(9) + fy (6, 4) * h '(9)
We know that g '(9) = −6; h '(9) = 4; fx (6, 4) = 9; fy (6, 4) = 1
Replacing:
(9 * -6) + (1 * 4) = -50
Por lo tanto dz / dt = -50
