Let $f ( x ) = \int _ { 3 x } ^ { 2 } \frac { \sin t } { t ^ { 2 } + 1 } d t . \text { Find } f ^ { \prime } ( x )$

question 26

Short Answer

Let $f ( x ) = \int _ { 3 x } ^ { 2 } \frac { \sin t } { t ^ { 2 } + 1 } d t . \text { Find } f ^ { \prime } ( x )$
A) $\frac { \sin 3 x } { 3 x ^ { 2 } + 1 }$

B) $- \frac { 3 \sin 3 x } { 3 x ^ { 2 } + 1 }$
C) $\frac { \cos x } { x ^ { 2 } + 1 }$
D) $- \frac { 3 \sin 3 x } { 9 x ^ { 2 } + 1 }$
E) $\frac { 3 \sin 3 x } { 9 x ^ { 2 } + 1 }$
F) $- \frac { \cos 3 x } { 9 x ^ { 2 } + 1 }$

G) $\frac { \cos x } { 2 x }$

H) $- \frac { \cos x } { 2 x }$

• A) \(\frac { \sin 3 x } { 3 x ^ { 2 } + 1 }\)

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Definitions:

Myringotome

A surgical instrument used for making an incision in the eardrum, typically to relieve pressure or allow drainage.

Myringotomy

A surgical procedure that involves making a small incision in the eardrum to relieve pressure or drain fluid.

Myringoplasty

Surgical repair of a hole or tear in the eardrum (tympanic membrane) to improve hearing and prevent water from entering the middle ear.

Auditory-Evoked Response

A measure of the brain's response to sound, used in hearing tests to assess auditory nerve and brainstem function.