[m]z`_{y}=(ln(3xy-4)`_{y}=\frac{1}{3xy-4}\cdot (3xy-4)`_{y}=\frac{1}{3xy-4}\cdot (3x)=\frac{3x}{3xy-4} [/m]
[m]z``_{xy}=(z`_{x})`_{y}=(\frac{3y}{3xy-4})`_{y}= \frac{(3y)`_{y}\cdot (3xy-4)-(3y)\cdot (3xy-4)`_{y}}{(3xy-4)^2}= \frac{3\cdot (3xy-4)-(3y)\cdot 3x}{(3xy-4)^2}=\frac{9xy-12-12xy}{(3xy-4)^2}=\frac{-3xy-12}{(3xy-4)^2} [/m]
[m]z`_{yx}=(z`_{y})`_{x}=(\frac{3x}{3xy-4})_{x}= \frac{(3x)`_{x}\cdot (3xy-4)-(3x)\cdot (3xy-4)`_{x}}{(3xy-4)^2}= \frac{3\cdot (3xy-4)-(3x)\cdot 3y}{(3xy-4)^2} =\frac{9xy-12-12xy}{(3xy-4)^2}=\frac{-3xy-12}{(3xy-4)^2}[/m]