Ask Question
19 September, 13:38

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.

+1
Answers (1)
  1. 19 September, 14:02
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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 ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers