Explanation Given information : The given production function is Q ( x , y ) = x a y b Formula used : The differentiation of two variables function following the rules of differentiation but treating either variable as a constant is known partial differentiation. Calculations: The given two variable function is Q ( x , y ) = x a y b ... (1) Differentiation Q ( x , y ) with respect to ‘ x’ keeping y as a constant, we have ∂ Q ∂ x = a x a − 1 y b ⇒ x ∂ Q ∂ x = a x a − 1 y b ⋅ x = a x a y b = a Q ( x , y ) ... (2) Differentiation Q ( x , y ) with respect to ‘ y’ keeping x as a constant, we have ∂ Q ∂ y = b x a y b − 1 ⇒ y ∂ Q ∂ y = b x a y b − 1 ⋅ y = b x a y b = b Q ( x , y )

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11, Problem 83SP

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Toshow:For a production function Q(x,y) : x∂Q∂x+y∂Q∂y=(a+b)Q , and x∂Q∂x+y∂Q∂y=Q , for b=1-a .

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Chapter 11, Problem 82SP

Chapter 11, Problem 84SP

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

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Chapter 11 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

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Toshow: For a production function Q ( x , y ) : x ∂ Q ∂ x + y ∂ Q ∂ y = ( a + b ) Q , and x ∂ Q ∂ x + y ∂ Q ∂ y = Q , for b =1- a .

Solution Summary: The author explains that the differentiation of two variables function following the rules of differentiation but treating either variable as a constant is known partial differentiation.

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Toshow:For a production function Q(x,y) : x∂Q∂x+y∂Q∂y=(a+b)Q , and x∂Q∂x+y∂Q∂y=Q , for b=1-a .

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Chapter 11 Solutions