Example (film) | Wiskunde op Tilburg University

We determine the second-order partial derivatives of $z(x,y)=ye^x+x^2y-5x$ .

$z'_x(x,y)=ye^x+2xy-5$
$z'_y(x,y)=e^x+x^2$

Hence,

$z''_{xx}(x,y)=ye^x+2y$
$z''_{yx}(x,y)=e^x+2x$
$z''_{xy}(x,y)=e^x+2x$
$z''_{yy}(x,y)=0$