\textbf{5.} Spo�t�te parci�ln� derivace 1. a 2. ��du funkce
    $u = \ln\left(x+y^2\right)$

    \textbf{�e�en�}
    \begin{align*}
        \frac{\partial u}{\partial x} &= \frac1{x+y^2}\\
        \frac{\partial u}{\partial y} &= \frac{2y}{x+y^2}\\
        \frac{\partial^2 u}{\partial x \partial y} &= -\frac{2y}{\left(x+y^2\right)^2}\\
        \frac{\partial^2 u}{\partial y \partial x} &= -\frac{2y}{\left(x+y^2\right)^2}\\
        \frac{\partial^2 u}{\partial x^2} &= -\frac1{\left(x+y^2\right)^2}\\
        \frac{\partial^2 u}{\partial y^2} &= \frac{-2y^2+2x}{\left(x+y^2\right)^2}
    \end{align*}
