Consider the equation $9sin(xy)4sin(xz)6sin(yz)=0.$ Find the values of $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}$ at the point $(-4,3,3).$

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}{|}_{(-4,3,3)}||=$

$($Simplify your answer. Type an exact answer, using radicals as needed.$)$ Solve both parts of the question.