Find the Derivative of the Function $$g ( x ) = \int _ { 1 } ^ { x } \frac { 1 } { t ^ { 2 } + 2 } d t$$

question 77

Multiple Choice

Find the derivative of the function.
$$g ( x ) = \int _ { 1 } ^ { x } \frac { 1 } { t ^ { 2 } + 2 } d t$$

• A)
• \(- \frac { 2 x } { \left( x ^ { 2 } + 2 \right) ^ { 2 } }\)
• B) \(- \frac { 2 } { 9 }\)
• C) \(\frac { 1 } { 3 }\)
• D) \(\frac { 1 } { x ^ { 2 } + 2 }\)

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Definitions:

Semicircular Canals

Structures in the inner ear involved in maintaining balance and sensing head rotation.

Cochlea

Spiral-shaped structure of the vertebrate inner ear containing the sensory receptors for hearing.

Inner Ear

Portion of the ear consisting of a vestibule, semicircular canals, and the cochlea where equilibrium is maintained and sound is transmitted.

Aqueous Humor

A clear fluid that fills the space in the front part of the eye between the lens and the cornea.