Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$

question 32

Multiple Choice

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. $y = \frac { 3 x - 6 } { ( x - 3 ) ( x - 1 ) ( x - 3 ) }$

• A) \(\frac { 3 ( x - 3 ) ( x - 1 ) ( x - 3 ) - \left( 3 x ^ { 2 } - 14 x + 15 \right) ( 3 x - 6 ) } { ( ( x - 3 ) ( x - 1 ) ( x - 3 ) ) ^ { 2 } }\)
• B) \(\frac { 3 ( x - 3 ) ( x - 1 ) ( x - 3 ) - \left( 3 x ^ { 2 } - 14 x + 15 \right) ( 3 x - 6 ) } { ( x - 3 ) ( x - 1 ) ( x - 3 ) }\)
• C) \(\frac { 3 ( x - 3 ) ( x - 1 ) ( x - 3 ) + \left( 3 x ^ { 2 } - 14 x + 7 \right) ( 3 x - 6 ) } { ( ( x - 3 ) ( x - 1 ) ( x - 3 ) ) ^ { 2 } }\)
• D) \(\frac { 3 ( x - 3 ) ( x - 3 ) - \left( 3 x ^ { 2 } - 14 x + 15 \right) } { ( ( x - 3 ) ( x - 3 ) ) ^ { 2 } }\)
• E) \(\frac { 3 } { 3 x ^ { 2 } - 14 x + 7 }\)

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Definitions:

Depressed Mood

A persistent feeling of sadness or a lack of interest in external stimuli, contributing significantly to the diagnosis of depression.

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A chronic form of depression characterized by a low mood over a long period.

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Pertaining to a mood characterized by deep sadness or gloominess, often associated with a type of depression.