Explanation Consider the given function, z ( x , y ) = tan x y . To find z x ( x , y ) , differentiate z ( x , y ) with respect to x by holding y . z x ( x , y ) = ∂ ∂ x ( tan x y ) = sec 2 x y ∂ ∂ x x y = y sec 2 x y Thus, z x ( x , y ) = y sec 2 x y . To find second derivate z x x ( x , y ) differentiate the z x ( x , y ) with respect to x by holding y . z x x ( x , y ) = ∂ ∂ x ( y sec 2 x y ) = y ∂ ∂ x ( sec 2 x y ) = 2 y 2 sec 2 x y tan x y To find z y ( x , y ) , differentiate z ( x , y ) with respect to y by holding x . z y ( x , y ) = ∂ ∂ y ( tan x y ) = sec 2 x y ∂ ∂ y x y = x sec 2 x y Thus, z y ( x , y ) = x sec 2 x y . To find second derivate z y y ( x , y ) , differentiate z y ( x , y ) with respect to y by holding x . z y y ( x , y ) = ∂ ∂ y ( x sec 2 x y ) = x ∂ ∂ y ( sec 2 x y ) = 2 x 2 sec 2 x y tan x y To find z y x ( x , y ) differentiate, z x ( x , y ) with respect to y by holding x

2nd Edition

ISBN: 9780321964038

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

Publisher: Pearson Addison Wesley,

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Chapter 9.2, Problem 36E

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The second-order partial derivatives for the function z=tanxy.

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Chapter 9.2, Problem 35E

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The second-order partial derivatives for the function z = tan x y .

Solution Summary: The author explains the second-order partial derivatives for the function z=mathrmtanxy.

To find:

The second-order partial derivatives for the function z=tanxy.

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Chapter 9 Solutions

The second-order partial derivatives for the function z = tan x y .

Solution Summary: The author explains the second-order partial derivatives for the function z=mathrmtanxy.

To find: The second-order partial derivatives for the function z=tanxy.

Want to see the full answer?

Chapter 9 Solutions

To find:

The second-order partial derivatives for the function z=tanxy.