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anonymous
 4 years ago
if z^3xzy=0 prove d^2z/dxdy=(3z^2+x)/(3z^2x)^3
anonymous
 4 years ago
if z^3xzy=0 prove d^2z/dxdy=(3z^2+x)/(3z^2x)^3

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[z^3xzy=0\]\[3z^2z'_xzxz'_x=0\quad\Rightarrow\quad z'_x=\frac{z}{3z^2x}\quad(1)\]\[3z^2z'_yxz'_y1=0\quad\Rightarrow\quad z'_y=\frac{1}{3z^2x}\quad(2)\]\[(2)\Rightarrow\quad 6zz'_xz'_y+3z^2z''_{xy}z'_yxz''_{xy}=0\]\[z''_{xy}=\frac{(16zz'_x)z'_y}{3z^2x}=\]\[=\frac{1}{3z^2x}\cdot\left(16z\frac{z}{3z^2x}\right)\cdot\frac{1}{3z^2x}=\]\[=\frac{3z^2x}{(3z^2x)^3}\]
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