Use the Chain Rule to Find $\frac { d w } { d t }$

question 50

Multiple Choice

Use the Chain Rule to find $\frac { d w } { d t }$ . $w = 3 x ^ { 6 } y ^ { 3 } z , \quad x = 6 t , \quad y = \cos 2 t , \quad z = t \sin t$

• A) \(3 x ^ { 5 } y ^ { 2 } ( 36 y z - 6 x z \sin 2 t + x y ( \sin t + t \cos t ) )\)
• B) \(3 x ^ { 6 } y ^ { 3 } ( 36 y z - 6 x z \sin 2 t + x y ( \sin t + t \cos t ) )\)
• C) \(648 x ^ { 5 } y ^ { 2 } \sin 2 t ( \sin t + t \cos t )\)
• D) \(648 x ^ { 6 } y ^ { 3 } z \sin 2 t ( \sin t + t \cos t )\)

---

Definitions:

Age Group

A range of ages into which individuals are categorized for analysis or reporting purposes, often used in demographics and marketing.

Clinic

A clinic is a healthcare facility primarily focused on the care of outpatients, often dedicated to a specific aspect of healthcare or targeted patient population.

Political Science

The study of government, political processes, institutions, and political behavior.

Liberal

A political and social philosophy that promotes individual freedoms, democracy, and a mixed economy with both government and private sector influences.