Chapter 14: Partial Derivatives - Section 14.3 - Partial Derivatives - Exercises 14.3 - Page 807: 16

$f_x=ye^{xy}ln(y)$ $f_y=e^{xy}\times1/y+xe^{xy}ln(y)$

Take the first partial derivatives of the given function. When taking partial derivative with respect to x, treat y as a constant, and vice versa: $f_x=ye^{xy}ln(y)$ $f_y=e^{xy}\times1/y+xe^{xy}ln(y)$