Use the Chain Rule to Find $\frac { \partial w } { \partial r }$

question 48

Multiple Choice

Use the Chain Rule to find $\frac { \partial w } { \partial r }$ and $\frac { \partial w } { \partial t }$ if $r = 5$ $s = 2$ and $t = 0$ $w = \frac { x ^ { 2 } y } { z ^ { 2 } } , \quad x = r e ^ { s t } , \quad y = s e ^ { n t } , \quad z = e ^ { r s t }$

• A) \(\frac { \partial w } { \partial r } = 20 , \quad \frac { \partial w } { \partial t } = - 550\)
• B) \(\frac { \partial w } { \partial r } = 100 , \quad \frac { \partial w } { \partial t } = 200\)
• C) \(\frac { \partial w } { \partial r } = 10 , \quad \frac { \partial w } { \partial t } = 0\)
• D) \(\frac { \partial w } { \partial r } = 7 , \quad \frac { \partial w } { \partial t } = - 550\)

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Definitions:

Regio-

A prefix denoting the region or position in a molecule where a chemical reaction occurs, often used in the context of regioselectivity.

Anti-Markovnikov Addition

A type of chemical addition reaction where the substituent is added to the less substituted carbon atom in a double bond or alkyne.

Peroxides

Chemical compounds containing an oxygen-oxygen single bond, or the peroxide anion O2^2-. They are often powerful oxidizing agents.

Stereochemical

Pertaining to the spatial arrangement of atoms in molecules and the effect of this arrangement on their chemical behavior.