\textbf{3.} Spo�t�te parci�ln� derivace 1. a 2. ��du funkce
    $u = x\sin(x+y)$

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