<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\textbf{4.} Spočtěte parciální derivace 1. a 2. řádu funkce
    $u = \frac x{y^2}$

    \textbf{Řešení}
    \begin{align*}
        \frac{\partial u}{\partial x} &amp;= \frac 1{y^3}\\
        \frac{\partial u}{\partial y} &amp;= \frac{-2x}{y^3}\\
        \frac{\partial^2 u}{\partial x \partial y} &amp;= -\frac2{y^3}\\
        \frac{\partial^2 u}{\partial y \partial x} &amp;= -\frac2{y^3}\\
        \frac{\partial^2 u}{\partial x^2} &amp;= 0\\
        \frac{\partial^2 u}{\partial y^2} &amp;= \frac{6x}{y^4}
    \end{align*}
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