Write a chain rule formula for the following derivative.
-$$\frac { \partial \mathrm { u } } { \partial \mathrm { r } } \text { for } \mathrm { u } = \mathrm { f } ( \mathrm { x } ) ; \mathrm { x } = \mathrm { g } ( \mathrm { p } , \mathrm { q } , \mathrm { r } )$$
A) $\frac { \partial \mathrm { u } } { \partial \mathrm { r } } = \frac { \mathrm { du } } { \mathrm { dx } } \frac { \partial \mathrm { x } } { \partial \mathrm { r } }$
B) $\frac { \partial u } { \partial r } = \frac { d u } { d x }$
C) $\frac { \partial \mathrm { u } } { \partial \mathrm { r } } = \frac { \partial \mathrm { x } } { \partial \mathrm { r } }$
D) $\frac { \partial u } { \partial r } = \frac { d u } { d x } \frac { \partial x } { \partial p } + \frac { d u } { d x } \frac { \partial x } { \partial q } + \frac { d u } { d x } \frac { \partial x } { \partial r }$

Question

Quizplus · Accepted Answer

The correct formula applies the chain rule for partial derivatives, where the derivative of $u$ with respect to $r$ is the product of the derivative of $u$ with respect to $x$ and the partial derivative of $x$ with respect to $r$.

Write a Chain Rule Formula for the Following Derivative A)