If u = e^ - x^2 - y^2 , then - Vidyadip

MCQ

If $u = {e^{ - {x^2} - {y^2}}}$, then

A
$x{u_x} = y{y_y}$
✓
$y{u_x} = x{u_y}$
C
$y{u_x} + x{u_y} = 0$
D
${x^2}{u_y} + {y^2}{u_x} = 0$

✓

Answer

Correct option: B.

$y{u_x} = x{u_y}$

b
(b) ${u_x} = {e^{ - {x^2} - {y^2}}}( - 2x) = - 2ux$,

${u_y} = {e^{ - {x^2} - {y^2}}}( - 2y) = - 2uy$

$y{u_x} = x{u_y}$.

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