Explanation It is given that the volume V is a function of h and r defined as V = 1 3 π h 2 ( 3 r − h ) . Differentiate V partially with respect to h as follows. ∂ V ∂ h = ∂ ∂ h ( 1 3 π h 2 ( 3 r − h ) ) = 1 3 π h 2 ∂ ∂ h ( 3 r − h ) + 1 3 π ( 3 r − h ) ∂ ∂ h ( h 2 ) = 1 3 π h 2 ( − 1 ) + 1 3 π ( 3 r − h ) ( 2 h ) = − 1 3 π h 2 + 2 3

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Chapter 29, Problem 44RE

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To find: The partial derivative ∂V∂h of the function V.

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Chapter 29, Problem 43RE

Chapter 29, Problem 45RE

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Chapter 29 Solutions

Basic Technical Mathematics

Ch. 29.1 - Practice Exercise If f(x, y) = 4xy2 – 3x2y, find...Ch. 29.1 - Prob. 1E Ch. 29.1 - Prob. 2E Ch. 29.1 - Prob. 3E Ch. 29.1 - Prob. 4E Ch. 29.1 - Prob. 5E Ch. 29.1 - Prob. 6E Ch. 29.1 - Prob. 7E Ch. 29.1 - Prob. 8E Ch. 29.1 - Prob. 9E

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The partial derivative ∂ V ∂ h of the function V .

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To find: The partial derivative ∂V∂h of the function V.

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Chapter 29 Solutions