Find the Gradient Vector for the Scalar Function $f ( x , y ) = \sin 4 x \cos 6 y$

question 49

Multiple Choice

Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) $f ( x , y ) = \sin 4 x \cos 6 y$

• A) \(\nabla f ( x , y ) = - 4 \cos ( 4 x ) \cos ( 6 y ) \hat { \mathbf { i } } + 6 \sin ( 4 x ) \sin ( 6 y ) \hat { \mathbf { j } }\)
• B) \(\nabla f ( x , y ) = 6 \cos ( 4 x ) \cos ( 6 y ) \hat { \mathbf { i } } - 4 \sin ( 4 x ) \sin ( 6 y ) \hat { \mathbf { j } }\)
• C) \(\nabla f ( x , y ) = 4 \cos ( 4 x ) \cos ( 6 y ) \hat { \mathbf { i } } + 6 \sin ( 4 x ) \sin ( 6 y ) \hat { \mathbf { j } }\)
• D) \(\nabla f ( x , y ) = 4 \cos ( 4 x ) \cos ( 6 y ) \hat { \mathbf { i } } - 6 \sin ( 4 x ) \sin ( 6 y ) \hat { \mathbf { j } }\)
• E) \(\nabla f ( x , y ) = - 6 \cos ( 4 x ) \cos ( 6 y ) \hat { \mathbf { i } } - 4 \sin ( 4 x ) \sin ( 6 y ) \hat { \mathbf { j } }\)

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Factory Overhead

The indirect costs associated with manufacturing, including indirect labor, indirect materials, and other expenses that cannot be directly tied to the production of goods.

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Items used in the production process that do not become a part of the final product, such as lubricants for machines.