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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.

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: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### 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.
Transcribed Image Text:### 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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