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^ ( √5 )₁ + ( 75 ) 1 15 S Show that the directional derivative of f(x, y, z) = z²x + y3 at (3, 9, 2) in the direction To find the directional derivative of f, we first need the gradient of fat (3, 9, 2). This is equal to '( √5)² . Therefore, the directional derivative of f(x, y, z) = z²x + y3 in the direction of jis 98√5. i+ 2 Next, we take the ---Select--- jis 98√5. ² (→ √ 5 ) ₁ + ( √²/5) ³. - j. This product is of this vector and the vector

^ ( √5 )₁ + ( 75 ) 1 15 S Show that the directional derivative of f(x, y, z) = z²x + y3 at (3, 9, 2) in the direction To find the directional derivative of f, we first need the gradient of fat (3, 9, 2). This is equal to '( √5)² . Therefore, the directional derivative of f(x, y, z) = z²x + y3 in the direction of jis 98√5. i+ 2 Next, we take the ---Select--- jis 98√5. ² (→ √ 5 ) ₁ + ( √²/5) ³. - j. This product is of this vector and the vector

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 2 Show that the directional derivative of f(x, y, z) = z²x + y³ at (3, 9, 2) in the direction ( √5) ₁ + (75) ₁ is is 98√/5. To find the directional derivative of f, we first need the gradient of fat (3, 9, 2). This is equal to Therefore, the directional derivative of f(x, y, z) = z²x + y³ in the direction of . Next, we take the ---Select--- 1 2 ( √5)i + (7/5)³ is is 98√/5. 1 2 ( √5)² + (²/5) i of this vector and the vector j. This product is
Transcribed Image Text:1 2 Show that the directional derivative of f(x, y, z) = z²x + y³ at (3, 9, 2) in the direction ( √5) ₁ + (75) ₁ is is 98√/5. To find the directional derivative of f, we first need the gradient of fat (3, 9, 2). This is equal to Therefore, the directional derivative of f(x, y, z) = z²x + y³ in the direction of . Next, we take the ---Select--- 1 2 ( √5)i + (7/5)³ is is 98√/5. 1 2 ( √5)² + (²/5) i of this vector and the vector j. This product is
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