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

Question

Quizplus · Accepted Answer

The Chain Rule is applied to differentiate $w$ with respect to $t$ by considering the partial derivatives of $w$ with respect to $x$, $y$, and $z$, and then multiplying by the derivatives of $x$, $y$, and $z$ with respect to $t$.

Use the Chain Rule to Find dwdt\frac { d w } { d t }dtdw​

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