Explanation Given that the function is z = 5 x + 4 x 2 y . Here, the dependent variable is z and the independent variables are x and y . Differentiate z partially with respect to x as follows. ∂ z ∂ x = ∂ ∂ x ( 5 x + 4 x 2 y ) = ∂ ∂ x ( 5 x ) + ∂ ∂ x ( 4 x 2 y ) = 5 + y ∂ ∂ x ( 4 x 2 ) + 4 x 2 ∂ ∂ x ( y ) use product rule = 5 + y ( 8 x ) + 4 x 2 ⋅ 0 That is, ∂ z ∂ x = 5 + 8 x y . Thus, the partial derivative of z with respect to x is 5 + 8 x y . Differentiate z partially with respect to y as follows

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Chapter 29.3, Problem 7E

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The partial derivatives of the function, ∂z∂x and ∂z∂y.

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Chapter 29.3, Problem 6E

Chapter 29.3, Problem 8E

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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 derivatives of the function, ∂ z ∂ x and ∂ z ∂ y .

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Chapter 29 Solutions