Find the Derivative of the Function $$y = \frac { ( x + 4 ) ( x + 1 ) } { ( x - 4 ) ( x - 1 ) }$$

question 541

Multiple Choice

Find the derivative of the function.
- $$y = \frac { ( x + 4 ) ( x + 1 ) } { ( x - 4 ) ( x - 1 ) }$$

• A) \(y ^ { \prime } = \frac { 10 x ^ { 2 } - 40 } { ( x - 4 ) ^ { 2 } ( x - 1 ) ^ { 2 } }\)
• B) \(y ^ { \prime } = \frac { 10 x - 40 } { ( x - 4 ) ^ { 2 } ( x - 1 ) ^ { 2 } }\)
• C) \(y ^ { \prime } = \frac { - 10 x ^ { 2 } + 40 } { ( x - 4 ) ^ { 2 } ( x - 1 ) ^ { 2 } }\)
• D) \(y ^ { \prime } = \frac { - x ^ { 2 } + 8 } { ( x - 4 ) ^ { 2 } ( x - 1 ) ^ { 2 } }\)

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Definitions:

Coefficient Of Correlation

A numerical measure that indicates the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

Linear Relationship

A type of correlation where the change in one variable is directly proportional to the change in another variable.

Shape

In statistics, refers to the geometric form of the distribution of a dataset or probability distribution, such as skewness and kurtosis defining its asymmetry and peakedness.

Unimodal

Describing a distribution with a single peak or mode, indicating the most frequently occurring value.