Find the Second Derivative of the Function $$p = \left( \frac { q + 4 } { q } \right) \left( \frac { q + 6 } { q ^ { 2 } } \right)$$

question 469

Multiple Choice

Find the second derivative of the function.
- $$p = \left( \frac { q + 4 } { q } \right) \left( \frac { q + 6 } { q ^ { 2 } } \right)$$

• A) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { \mathrm { dq } ^ { 2 } } = - \frac { 2 } { \mathrm { q } ^ { 3 } } - \frac { 60 } { \mathrm { q } ^ { 4 } } - \frac { 288 } { \mathrm { q } ^ { 5 } }\)
• B) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { d \mathrm { q } ^ { 2 } } = - \frac { 1 } { \mathrm { q } ^ { 2 } } - \frac { 20 } { \mathrm { q } ^ { 3 } } - \frac { 72 } { \mathrm { q } ^ { 4 } }\)
• C) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { d q ^ { 2 } } = \frac { 2 } { \mathrm { q } } + \frac { 60 } { \mathrm { q } ^ { 2 } } + \frac { 288 } { \mathrm { q } ^ { 3 } }\)
• D) \(\frac { \mathrm { d } ^ { 2 } \mathrm { p } } { d q ^ { 2 } } = \frac { 2 } { \mathrm { q } ^ { 3 } } + \frac { 60 } { \mathrm { q } ^ { 4 } } + \frac { 288 } { \mathrm { q } ^ { 5 } }\)

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Definitions:

Structural Features

Aspects of a chemical compound's architecture, including the arrangement of atoms and the bonds connecting them.

Triple Bonds

A chemical bond in which three pairs of electrons are shared between two atoms, resulting in a strong and linear connection.

Molecules

The smallest units of a chemical compound that can exist while retaining the identity and chemical properties of the compound.

Elements of Unsaturation

The count of the unsaturation within a molecule, signified by double bonds, triple bonds, or rings that reduce the number of hydrogen atoms relative to a saturated alkane.