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

question 98

Multiple Choice

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

• 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) \(648 x ^ { 6 } y ^ { 3 } z \sin 2 t ( \sin t + t \cos t )\)

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