$\text { Find the derivative of the function } f ( x ) = \ln \left( \frac { 3 x } { x ^ { 2 } + 4 } \right) \text {. }$

question 46

Multiple Choice

$\text { Find the derivative of the function } f ( x ) = \ln \left( \frac { 3 x } { x ^ { 2 } + 4 } \right) \text {. }$

• A) \(f ^ { t } ( x ) = \frac { 1 } { x } + \frac { 2 x } { x ^ { 2 } + 4 }\)
• B)\(f ^ { t} ( x ) = \frac { 4 - x ^ { 2 } } { x \left( x ^ { 2 } + 4 \right) }\)
• C)\(f ^ { t} ( x ) = \frac { 1 } { x } - \frac { 2 x } { x ^ { 2 } + 4 }\)
• D) \(f ^ { t } ( x ) = \frac { 3 } { x } + \frac { 2 x } { x ^ { 2 } + 4 }\)
• E) \(f ^ { t } ( x ) = \frac { 1 } { 3 x } - \frac { 2 x } { x ^ { 2 } + 4 }\)

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Definitions:

Vernix

A greasy, white substance that covers and protects the skin of a fetus while in the womb and is still present at birth in most cases.

Newborns

Infants from birth to about 2 months of age, characterized by rapid physical growth and development in the initial stages of life.

Miscarriage

The spontaneous loss of a pregnancy before the 20th week, often due to underlying health issues or genetic problems.

Stillbirth

The death of a baby before or during delivery.