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

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Definitions:

Meninges

The three layers of protective tissue (dura mater, arachnoid mater, and pia mater) covering the brain and spinal cord.

Arachnoid

A delicate membrane that encloses the brain and spinal cord, situated between the dura mater and pia mater.

Pia

Short for pia mater, it is the delicate innermost membrane enveloping the brain and spinal cord.