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

question 30

Multiple Choice

Use the Chain Rule to find $\frac { d w } { d t }$ $w = 9 x ^ { 4 } y ^ { 3 } z , \quad x = 6 t , \quad y = \cos 7 t , \quad z = t \sin t$

• A) \(4,536 x ^ { 4 } y ^ { 3 } z \sin 7 t ( \sin t + t \cos t )\)
• B) \(9 x ^ { 4 } y ^ { 3 } ( 24 y z - 21 x z \sin 7 t + x y ( \sin t + t \cos t ) )\)
• C) \(4,536 x ^ { 3 } y ^ { 2 } \sin 7 t ( \sin t + t \cos t )\)
• D) \(9 x ^ { 3 } y ^ { 2 } ( 24 y z - 21 x z \sin 7 t + x y ( \sin t + t \cos t ) )\)

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Definitions:

Means

Statistical measures that represent the central point or average value of a dataset.

Marginal Means

The mean values of a variable across different levels of another variable, often used in the analysis of variance.

Main Effect

The direct influence of an independent variable on a dependent variable in an experimental study, ignoring the effects of other variables.

Marginal Means

The average value of a variable at each level of another variable, often used in the analysis of variance.