Write a chain rule formula for the following derivative.
-$\frac { \partial w } { \partial x }$ for $w = f ( p , q ) ; p = g ( x , y ) , q = h ( x , y )$
A) $\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } \frac { \partial p } { \partial x } + \frac { \partial w } { \partial q } \frac { \partial q } { \partial x }$
B) $\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } \frac { \partial p } { \partial x }$
C) $\frac { \partial w } { \partial x } = \frac { \partial w } { \partial x } \frac { \partial x } { \partial p } + \frac { \partial w } { \partial x } \frac { \partial x } { \partial q }$
D) $\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } + \frac { \partial w } { \partial q }$

Question

Quizplus · Accepted Answer

The chain rule states that the derivative of a composite function is equal to the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. Using this rule twice for the variables p and q and substituting into the original equation for w, we get:

$\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } \frac { \partial p } { \partial x } + \frac { \partial w } { \partial q } \frac { \partial q } { \partial x }$

Therefore, the correct answer is A.

Write a Chain Rule Formula for the Following Derivative ∂w∂x\frac { \partial w } { \partial x }∂x∂w​

Write a Chain Rule Formula for the Following Derivative $\frac { \partial w } { \partial x }$