Show all working and explanation. (b) State the rule(s) of differentiation that is most appropriate, explain why anddifferentiate each of the following:(i) f(x) = (x + 1)³(6 − x)² ³√√2x + 1(ii)f(x) =-3x (x+2)³√3x-5(c) Use partial derivatives to determine if the demand functions for two commoditiesrepresent a substitute, complement or neither.D₁ = 2000 +100P₁ + 2D₂ = 1500 +25P2P₂P₁ + 7

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Answered: (b) State the rule(s) of…

(b) State the rule(s) of differentiation that is most appropriate, explain why and differentiate each of the following: (1) f(x) = (x + 1)³(6-x)² √2x + 1 (ii) f(x): -3x (x+2)³ √3x-5

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Question

Show all working and explanation.

(b) State the rule(s) of differentiation that is most appropriate, explain why and
differentiate each of the following:
(i) f(x) = (x + 1)³(6 − x)² ³√√2x + 1
(ii)
f(x) =
-3x (x+2)³
√3x-5
(c) Use partial derivatives to determine if the demand functions for two commodities
represent a substitute, complement or neither.
D₁ = 2000 +
100
P₁ + 2
D₂ = 1500 +
25P2
P₂
P₁ + 7

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