A) B) C) $\frac { d y } { d x } = \frac { 1 } { 7 } \cdot \left( \frac { 1 } { ( x + 7 ) ^ { 2 } } + \frac { 4 x } { x ^ { 2 } + 16 } \right)$

question 52

Multiple Choice

$\text { Find the derivative of the function } y = \arctan \left( \frac { x } { 7 } \right) + \frac { 4 x - 6 } { 7 \left( x ^ { 2 } + 4 \right) } \text {. }$

• A)\(\frac { d y } { d x } = \frac { 1 } { 7 } \cdot \left( \frac { 1 } { x + 49 } + \frac { 16 - 12 x - 4 x ^ { 2 } } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } \right)\)
• B)\(\frac { d y } { d x } = \frac { 1 } { 7 } \cdot \left( \frac { 1 } { 1 + ( x / 7 ) ^ { 2 } } + \frac { 16 + 12 x - 4 x ^ { 2 } } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } \right)\)
• C) \(\frac { d y } { d x } = \frac { 1 } { 7 } \cdot \left( \frac { 1 } { ( x + 7 ) ^ { 2 } } + \frac { 4 x } { x ^ { 2 } + 16 } \right)\)
• D)\(\frac { d y } { d x } = \frac { 1 } { 7 } \cdot \left( \frac { 1 } { x + 49 } + \frac { 16 + 12 x - 4 x ^ { 2 } } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } \right)\)
• E)\(\frac { d y } { d x } = \frac { 1 } { 7 } \cdot \left( \frac { 1 } { x + 49 } + \frac { 4 x } { \left( x ^ { 2 } + 4 \right) ^ { 2 } } \right)\)

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Definitions:

Assimilation

The process by which individuals or groups adopt the customs, attitudes, and norms of a dominant or surrounding culture, often losing original identity characteristics.

Group Metamorphosis

The process by which a group evolves and changes its structure, behavior, or identity over time.

Study of Whiteness

A field of scholarly research that examines the social construction of whiteness as a racial identity and its implications for power and privilege.

Power

The ability or capacity to do something or act in a particular way, especially as a faculty or quality.