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

Question 118

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Let f(x,y)={x2x+y if (x,y)(0,0)0 if (x,y)=(0,0)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 δfδx\frac { \delta f } { \delta x } and δfδy\frac { \delta f } { \delta y } .(b) Find the value of the above derivatives at (0,0)( 0,0 ) , if they exist.

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