If z= ( x+ y) , then ( 2 x) z x +( 2 y) z y is equal to

Step-by-step solution

z= ( x+ y) On differentiating partially w.r.t. x and y , we get and aligned z x & = 1 ^2 x x+ y and z y & = ^2 y x+ y aligned Now, aligned & 2 x z x + 2 y z y & = 2 x ^2 x+ 2 y ^2 y x+ y & = 2 x x 1 ^2 x +2 y y 1 ^2 y x+ y & = 2[ x+ y] x+ y & =2 aligned