Find the Derivative of the Function $$r = \frac { \sqrt { \theta } - 3 } { \sqrt { \theta } + 3 }$$

question 229

Multiple Choice

Find the derivative of the function.
- $$r = \frac { \sqrt { \theta } - 3 } { \sqrt { \theta } + 3 }$$

• A) \(r ^ { \prime } = \frac { 6 } { ( \theta + 3 ) \sqrt { \theta ^ { 2 } - 9 } }\)
• B) \(r ^ { \prime } = - \frac { 3 } { \sqrt { \theta } ( \theta + 3 ) ^ { 2 } }\)
• C) \(\mathrm { r } ^ { \prime } = \frac { 3 } { \theta + 3 }\)
• D) \(r ^ { \prime } = \frac { 3 } { \sqrt { \theta } ( \theta + 3 ) ^ { 2 } }\)

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Definitions:

One-group Pretest-posttest Design

A research design in which a single group is measured or tested before and after an intervention to assess change.

Participants Change

The phenomenon where individuals in a study alter their behavior or responses due to awareness of being observed or other study factors.

Time

A continuous sequence of events, perceived by its passage and measurable in hours, minutes, and seconds.

Experimental Manipulation

The process of intentionally changing a variable in an experiment to study its effects on other variables.