Find the directional derivative of f(x, y) = x²y³ + 2x¹y at the point (4, 4) in the direction 0 = 2π/3. The gradient of fƒ is: Vƒ = (2xy³ + 8x³y Vƒ(4,4)= (2560 The directional derivative is: 1280+640sqrt(3) 3x²y² + 2x4 1280 )

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.CR: Chapter 4 Review
Problem 4CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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You have answered 4 out of 5 parts correctly. 3 attempts remaining.
Find the directional derivative of ƒ(x, y) = x²y³ + 2x¹y at the point (4, 4) in the direction 0 = 27/3.
The gradient of f is:
Vƒ = ( 2xy³ + 8x³y
Vƒ(4,4)= (2560
The directional derivative is:
1280+640sqrt(3)
·3x²₁²+2x4
1280
Transcribed Image Text:You have answered 4 out of 5 parts correctly. 3 attempts remaining. Find the directional derivative of ƒ(x, y) = x²y³ + 2x¹y at the point (4, 4) in the direction 0 = 27/3. The gradient of f is: Vƒ = ( 2xy³ + 8x³y Vƒ(4,4)= (2560 The directional derivative is: 1280+640sqrt(3) ·3x²₁²+2x4 1280
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