If z = f (x, y), where f is differentiable, and x = g (t) y = h (t) g (9) = 6 h (9) = 4 g' (9) = - 6 h' (9) = 4 fx (6, 4) = 9 fy (6, 4) = 1 find dz/dt when t = 9.

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