99 Percentile Qs Bank for JEE MainMathematicsDifferentiation

If u(x, y)=y x+x y , then u_x u_y-u_x x-u_y y+ x y is equal to :

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Correct answer

C. 1

Step-by-step solution

We have, u(x, y)=y x+x y On differentiating partially w.r.t. x and y respectively, u_x= y x + y, u_y= x+ x y Now, u_x u_y-u_x x-u_y y+ x y= ( y x + y ) ( x+ x y )- ( y x + y ) x- ( x+ x y ) y+ x y=1+ y x x+ x y y+ x y- y x x- x y- x y- x y y+ x y=1

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