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\textbf{Partial Differentiation}

\textit{\textbf{Functions of more than one variable}}
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\textbf{Question}

Specify the domain of the function.

$$f(x,y,z) = \frac{e^{xyz}}{\sqrt{xyz}}$$


\textbf{Answer}

The domain consists of all points $(x,y,z)$ where $xyz&gt;0$. i.e all
points in the four octants:
\begin{eqnarray*}
x &amp; &gt; &amp; 0, \ y&gt;0, \ z&gt;0\\
x &amp; &gt; &amp; 0, \ y&lt;0, \ z&lt;0\\
x &amp; &lt; &amp; 0, \ y&gt;0, \ z&lt;0\\
x &amp; &lt; &amp; 0, \ y&lt;0, \ z&gt;0\\
\end{eqnarray*}


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