Find the Second Derivative of the Function $$p = \left( \frac { q + 3 } { q } \right) \left( \frac { q + 5 } { q ^ { 2 } } \right)$$

question 68

Multiple Choice

Find the second derivative of the function.
- $$p = \left( \frac { q + 3 } { q } \right) \left( \frac { q + 5 } { q ^ { 2 } } \right)$$

• A) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { \mathrm { dq } ^ { 2 } } = \frac { 2 } { \mathrm { q } } + \frac { 48 } { \mathrm { q } ^ { 2 } } + \frac { 180 } { \mathrm { q } ^ { 3 } }\)
• B) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { \mathrm { dq } ^ { 2 } } = \frac { 2 } { \mathrm { q } ^ { 3 } } + \frac { 48 } { \mathrm { q } ^ { 4 } } + \frac { 180 } { \mathrm { q } ^ { 5 } }\)
• C) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { \mathrm { dq } ^ { 2 } } = - \frac { 2 } { \mathrm { q } ^ { 3 } } - \frac { 48 } { \mathrm { q } ^ { 4 } } - \frac { 180 } { \mathrm { q } ^ { 5 } }\)
• D) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { \mathrm { dq } ^ { 2 } } = - \frac { 1 } { \mathrm { q } ^ { 2 } } - \frac { 16 } { \mathrm { q } ^ { 3 } } - \frac { 45 } { \mathrm { q } ^ { 4 } }\)

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