Give an appropriate answer.
-$$f ( x , y ) = \frac { x } { x + y }$$
A) $\frac { \partial f } { \partial x } = \frac { 2 x + y } { ( x + y ) ^ { 2 } } ; \frac { \partial f } { \partial y } = \frac { x } { ( x + y ) ^ { 2 } }$
B) $\frac { \partial f } { \partial x } = \frac { y } { ( x + y ) ^ { 2 } } ; \frac { \partial f } { \partial y } = - \frac { x } { ( x + y ) ^ { 2 } }$
C) $\frac { \partial f } { \partial x } = - \frac { y } { ( x + y ) ^ { 2 } } ; \frac { \partial f } { \partial y } = - \frac { x } { ( x + y ) ^ { 2 } }$
D) $\frac { \partial f } { \partial x } = \frac { 2 x + y } { ( x + y ) ^ { 2 } } ; \frac { \partial f } { \partial y } = - \frac { x } { ( x + y ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The correct partial derivatives of $f(x, y) = \frac{x}{x + y}$ are $\frac{\partial f}{\partial x} = \frac{y}{(x + y)^2}$ and $\frac{\partial f}{\partial y} = -\frac{x}{(x + y)^2}$, which are found using the quotient rule for differentiation.

Give an Appropriate Answer f(x,y)=xx+yf ( x , y ) = \frac { x } { x + y }f(x,y)=x+yx​

Give an Appropriate Answer $f ( x , y ) = \frac { x } { x + y }$