Answer
$ye^{xy }\space \ln(y)$ and $e^{xy} (\dfrac{1}{y}+x \ln y)$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $x$, by keeping $y$ as a constant.
$f_x=ye^{xy }\space \ln(y)$
Our aim is to take the first partial derivatives of the given function $f(x,y)$ with respect to $y$, by keeping $x$ as a constant.
$f_y=e^{xy}\times \dfrac{1}{y}+xe^{xy}ln(y)$= $e^{xy} (\dfrac{1}{y}+x \ln y)$
