I'm stuck on this one. I need help please & thank you!! ### Problem: Directional DerivativeFind the directional derivative of $ f(x, y, z) = xy + z^3 $ at the point $ P = (3, -4, -3) $ in the direction pointing to the origin.(Give an exact answer. Use symbolic notation and fractions where needed.)---This problem involves computing the directional derivative, which measures the rate of change of a function as you move in a specific direction. The function given is $ f(x, y, z) = xy + z^3 $. The point of interest is $ P = (3, -4, -3) $, and the direction is towards the origin $(0, 0, 0)$. The directional derivative in this context will provide valuable insight into how the function changes as we move towards the origin from the specified point.

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Answered: Find the directional derivative of f(x,…

Find the directional derivative of f(x, y, z) = xy + z³ at the point P = (3,-4, -3) in the direction pointing to the origin.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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I'm stuck on this one. I need help please & thank you!!

### Problem: Directional Derivative

Find the directional derivative of $ f(x, y, z) = xy + z^3 $ at the point $ P = (3, -4, -3) $ in the direction pointing to the origin.

(Give an exact answer. Use symbolic notation and fractions where needed.)

---

This problem involves computing the directional derivative, which measures the rate of change of a function as you move in a specific direction. The function given is $ f(x, y, z) = xy + z^3 $. The point of interest is $ P = (3, -4, -3) $, and the direction is towards the origin $(0, 0, 0)$. The directional derivative in this context will provide valuable insight into how the function changes as we move towards the origin from the specified point.

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