Find the Derivative of the Function $f ( x ) = x ^ { 8 } \sqrt { 2 - 2 x }$

question 41

Multiple Choice

Find the derivative of the function. $f ( x ) = x ^ { 8 } \sqrt { 2 - 2 x }$

• A) \(f ^ { \prime } ( x ) = \frac { x ^ { 7 } ( 32 - 34 x ) } { 2 \sqrt { 2 - 2 x } }\)
• B) \(f ^ { \prime } ( x ) = \frac { x ^ { 7 } ( 32 + 34 x ) } { 2 \sqrt { 2 - 2 x } }\)
• C) \(f ^ { \prime } ( x ) = \frac { x ^ { 7 } ( 2 - 34 x ) } { 2 \sqrt { 2 - 2 x } }\)
• D) \(f ^ { \prime } ( x ) = \frac { x ^ { 7 } ( 32 - 2 x ) } { 2 \sqrt { 2 - 2 x } }\)
• E) \(f ^ { \prime } ( x ) = \frac { x ^ { 7 } ( 2 + 2 x ) } { 2 \sqrt { 2 - 2 x } }\)

---

Definitions:

Cage

A structure of bars or wires in which animals or birds are confined.

Confounding Variable

A variable outside of the researcher's control that can affect the results of a study, potentially leading to misleading conclusions.

Lurking

In statistics, a lurking variable is one that is not directly observed but can influence the relationship between the studied variables.

Explanatory Variable

A variable that is manipulated or observed to determine its effects on a dependent variable in an experimental or observational study.