Differentiate $y = x \arctan ( 3 x )$
A) $y ^ { t } = \frac { 3 x } { \left( 1 + ( 3 x ) ^ { 2 } \right) } + \arctan ( 3 x )$

question 25

Multiple Choice

Differentiate $y = x \arctan ( 3 x )$ .

• A) \(y ^ { t } = \frac { 3 x } { \left( 1 + ( 3 x ) ^ { 2 } \right) } + \arctan ( 3 x )\)
• B) \(y ^ { \prime } = \frac { 1 } { 3 + x ^ { 2 } } + 3 \arctan ( 3 x )\)
• C) \(y ^ { \prime } = 3 \arctan ( 3 x )\)
• D) \(y ^ { t } = 1 \cdot \arctan ( 3 x )\)

---

Definitions:

Expansion Phase

A period in the business cycle during which the economy grows and unemployment decreases.

World War II

A global conflict that lasted from 1939 to 1945, involving most of the world's nations, including all of the great powers, organized into two opposing military alliances: the Allies and the Axis.

Recessions

Instances of provisional economic weakness where both trading and industrial activities fall off, universally determined by a two-quarter continuous drop in GDP.

General Merchandise

A category of goods that includes a wide range of products from apparel to home goods sold by retailers.