Explanation Given expression is R c = a c 2 1 + b c 2 - k c . where, R c = measures the release of calcium c = The amount of free calcium outside the vehicles in which it is stored; a , b , and k are positive constants given equation is simplified as below, R c = a c 2 - k c 1 + b c 2 1 + b c 2 R c = a c 2 - k c + k b c 3 1 + b c 2 R c = a c 2 - k c - k b c 3 1 + b c 2 Definition of the Quotient Rule: If f ( x ) = u ( x ) v ( x ) , and if all indicated derivative exists, and if v ( x ) ≠ 0 , then f ' x = v ( x ) · u ' x - u ( x ) · v ' x v ( x ) 2 The derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. Based on the above quotient rule, Let us consider, f ( x ) = R c u ( x ) = u ( c ) = a c 2 - k c - k b c 3 v ( x ) = v ( c ) = 1 + b c 2 Then, f ' x = R ' c According to the Power Rule and Constant Rule, u ' c and v ' c can be written as below, u ' c = a 2 c 2 - 1 - k c 1 - 1 - k b 3 c 3 - 1 u ' c = 2 a c - k - 3 k b c 2 Similarly, v ' c = 0 + b 2 c 2 - 1 = 2 b c v ' c = 2 b c Substituting f ' x = R ' c , u ' x = 2 a c - k - 3 k b c 2 , v ' x = 2 b c , u ( x ) = a c 2 - k c - k b c 3 and v ( x ) = ( 1 + b n 2 ) in the below function, f ' x = v ( x ) · u ' x - u ( x ) · v ' x v ( x ) 2 R ' c = 1 + b c 2 · 2 a c - k - 3 k b c 2 - a c 2 - k c - k b c 3 · 2 b c 1 + b c 2 2 Simplifying the above function, R ' c = 2 a c - k - 3 k b c

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ISBN: 9780321964038

Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher: Pearson Addison Wesley,

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Chapter 4.2, Problem 47E

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R'c and interpret accordingly, where Rc=ac21+bc2-kc.

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Chapter 4.2, Problem 46E

Chapter 4.2, Problem 48E

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R ' c and interpret accordingly, where R c = a c 2 1 + b c 2 - k c .

Solution Summary: The author explains that R'(c)=ac

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To find:

R'c and interpret accordingly, where Rc=ac21+bc2-kc.

Want to see the full answer?

Chapter 4 Solutions

R ' c and interpret accordingly, where R c = a c 2 1 + b c 2 - k c .

Solution Summary: The author explains that R'(c)=ac

Videos

To find: R'c and interpret accordingly, where Rc=ac21+bc2-kc.

Want to see the full answer?

Chapter 4 Solutions

To find:

R'c and interpret accordingly, where Rc=ac21+bc2-kc.