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

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Question

(B) Given $u = e^{-x^2 - y^2}$.First,find the partial derivative of $u$ with respect to $x$:$u_x = \frac{\partial u}{\partial x} = e^{-x^2 - y^2} \cdo

Vedclass · Accepted Answer

$y u_x = x u_y$

Vedclass · Answer

(B) Given $u = e^{-x^2 - y^2}$.First,find the partial derivative of $u$ with respect to $x$:$u_x = \frac{\partial u}{\partial x} = e^{-x^2 - y^2} \cdot (-2x) = -2x u$.Next,find the partial derivative of $u$ with respect to $y$:$u_y = \frac{\partial u}{\partial y} = e^{-x^2 - y^2} \cdot (-2y) = -2y u$.Now,consider the expression $y u_x$:$y u_x = y(-2x u) = -2xy u$.Consider the expression $x u_y$:$x u_y = x(-2y u) = -2xy u$.Comparing both,we get $y u_x = x u_y$.

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

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