[m]\frac{ ∂z }{ ∂x }=z`_{x}=(x^2\cdot e^{3y+x})`_{x}= (x^2)`\cdot e^{3y+x}+x^2\cdot (e^{3y+x})`_{x}=2x\cdot e^{3y+x}+x^2\cdot e^{3y+x}\cdot (3y+x)`_{x}=2x\cdot e^{3y+x}+x^2\cdot e^{3y+x}\cdot 1=e^{3y+x}\cdot (2x+x^2)[/m]
[m]\frac{ ∂z }{ ∂y }=z`_{y}=(x^2\cdot e^{3y+x})`_{y}= x^2\cdot (e^{3y+x})`_{y}=x^2\cdot e^{3y+x}\cdot (3y+x)`_{y}=x^2\cdot e^{3y+x}\cdot 3=3x^2\cdot e^{3y+x}[/m]