Find the Second Derivative of the Function $$y = \frac { ( x - 6 ) \left( x ^ { 2 } + 3 x \right) } { x ^ { 3 } }$$

question 171

Multiple Choice

Find the second derivative of the function.
- $$y = \frac { ( x - 6 ) \left( x ^ { 2 } + 3 x \right) } { x ^ { 3 } }$$

• A) \(\frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { 6 } { x } - \frac { 108 } { x ^ { 2 } }\)
• B) \(\frac { \mathrm { d } ^ { 2 } y } { d x ^ { 2 } } = \frac { 3 } { x ^ { 2 } } + \frac { 36 } { x ^ { 3 } }\)
• C) \(\frac { \mathrm { d } ^ { 2 } y } { d x ^ { 2 } } = - \frac { 6 } { x ^ { 3 } } - \frac { 108 } { x ^ { 4 } }\)
• D) \(\frac { d ^ { 2 } y } { d x ^ { 2 } } = \frac { 6 } { x ^ { 3 } } + \frac { 108 } { x ^ { 4 } }\)

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