[m]\frac{ ∂z }{ ∂x }=z`_{x}=(e^{xy}\cdot ln(x+y))`_{x}= (e^{xy})`_{x}\cdot ln(x+y)+e^{xy}\cdot ( ln(x+y))`_{x}=e^{xy}\cdot (xy)`_{x}\cdot ln(x+y)+e^{xy}\cdot\frac{1}{x+y}\cdot (x+y)`_{x}=[/m]
[m]=e^{xy}\cdot (y)\cdot ln(x+y)+e^{xy}\cdot\frac{1}{x+y}\cdot 1=y\cdot e^{xy}\cdot ln(x+y)+e^{xy}\cdot\frac{1}{x+y}[/m]
[m]\frac{ ∂z }{ ∂y }=z`_{y}=(e^{xy}\cdot ln(x+y))`_{y}= (e^{xy})`_{y}\cdot ln(x+y)+e^{xy}\cdot ( ln(x+y))`_{y}=e^{xy}\cdot (xy)`_{y}\cdot ln(x+y)+e^{xy}\cdot\frac{1}{x+y}\cdot (x+y)`_{y}=[/m]
[m]=e^{xy}\cdot (x)\cdot ln(x+y)+e^{xy}\cdot\frac{1}{x+y}\cdot 1=x\cdot e^{xy}\cdot ln(x+y)+e^{xy}\cdot\frac{1}{x+y}[/m]