Explanation Given: The expression is given as p = 5000 − q 2 20 . Also, the value of q is 5 . Formula used: Chain Rule: If f and g are functions and y = [ g ( x ) ] , then y ′ = f ′ [ g ( x ) ] ⋅ g ′ ( x ) provided that f ′ [ g ( x ) ] and g ′ ( x ) exists. Calculation: Implicit Differentiation is used to evaluate d q d p , when q is defined implicitly as a function of p . The differentiation is carried out in two steps: Step 1: Both the sides of the given equation is differentiated with respect to p . Since, q is the function of p , so always use the chain rule. In this case, differentiate the equation with respect to p . d d p ( p ) = d d p ( 5000 − q 2 20 ) d d p ( p )

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Chapter 12.4, Problem 39E

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To calculate: dqdp for the given expression p=5000−q220.

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Chapter 12.4, Problem 38E

Chapter 12.4, Problem 40E

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Pearson eText for Mathematics with Applications In the Management, Natural, and Social Sciences -- Instant Access (Pearson+)

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d q d p for the given expression p = 5000 − q 2 20 .

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