Let $f ( x , y ) = \left\{ \begin{array} { l l }
\frac { x ^ { 2 } } { x + y } & \text { if } ( x , y ) \neq ( 0,0 ) \
0 & \text { if } ( x , y ) = ( 0,0 )
\end{array} \right.$ (a) Find $\frac { \delta f } { \delta x }$ and $\frac { \delta f } { \delta y }$ .(b) Find the value of the above derivatives at $( 0,0 )$ , if they exist.

Question

Let $f ( x , y ) = \left\{ \begin{array} { l l } 
\frac { x ^ { 2 } } { x + y } & \text { if } ( x , y ) \neq ( 0,0 ) \
0 & \text { if } ( x , y ) = ( 0,0 )
\end{array} \right.$ (a) Find $\frac { \delta f } { \delta x }$ and $\frac { \delta f } { \delta y }$ .(b) Find the value of the above derivatives at $( 0,0 )$ , if they exist.

Quizplus · Accepted Answer

The Answer of Let $f ( x , y ) = \left\{ \begin{array} { l l } 
\frac { x ^ { 2 } } { x + y } & \text { if } ( x , y ) \neq ( 0,0 ) \
0 & \text { if } ( x , y ) = ( 0,0 )
\end{array} \right.$ (a) Find $\frac { \delta f } { \delta x }$ and $\frac { \delta f } { \delta y }$ .(b) Find the value of the above derivatives at $( 0,0 )$ , if they exist.

Let (A) Find δfδx\frac { \delta f } { \delta x }δxδf​

Let (A) Find $\frac { \delta f } { \delta x }$