if $$ z= an ^{-1}\left(\frac{x+y}{\sqrt{x}+\sqrt{y}} ight) $$ then shan that $$ x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=\frac{1}{4} \sin 2 z $$.

Question

if $$ z=	an ^{-1}\left(\frac{x+y}{\sqrt{x}+\sqrt{y}}ight) $$ then shan that $$ x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=\frac{1}{4} \sin 2 z $$.

Stephens Bowman · Accepted Answer

$$ x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y} = \frac{1}{4} \sin 2z $$

if \( z=\tan ^{-1}\left(\frac{x+y}{\sqrt{x}+\sqrt{y}}\right) \) then shan that \( x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=\frac{1}{4} \sin 2 z \).

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Solución paso a paso

if \( z=\tan ^{-1}\left(\frac{x+y}{\sqrt{x}+\sqrt{y}}\right) \) then shan that \( x \frac{\partial z}{\partial x}+y \frac{\partial z}{\partial y}=\frac{1}{4} \sin 2 z \).

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Solución paso a paso

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