Find the Derivative of the Function $$g ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 6 x }$$

question 120

Multiple Choice

Find the derivative of the function.
- $$g ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } + 6 x }$$

• A) \(g ^ { \prime } ( x ) = \frac { 2 x ^ { 3 } - 5 x ^ { 2 } - 30 x } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)
• B) \(g ^ { \prime } ( x ) = \frac { x ^ { 4 } + 6 x ^ { 3 } + 5 x ^ { 2 } + 30 x } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)
• C) \(g ^ { \prime } ( x ) = \frac { 4 x ^ { 3 } + 18 x ^ { 2 } + 10 x + 30 } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)
• D) \(g ^ { \prime } ( x ) = \frac { 6 x ^ { 2 } - 10 x - 30 } { x ^ { 2 } ( x + 6 ) ^ { 2 } }\)

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Definitions:

Outliers

Observations in a dataset that lie at an abnormal distance from other values, often indicating variability in a measurement, experimental errors, or novelty.

Lower Quartile

The value below which 25% of the data in a dataset falls, also known as the first quartile.

Upper Quartile

The median of the upper half of a dataset, marking the 75th percentile.

Right-Skewed

A distribution that has a longer tail on the right side of the peak, indicating that the majority of the data points lie to the left of the mean.