Consider the equation $6sin(xy)9sin(xz)7sin(yz)=0.$ 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 $(-2,-4,-4).$

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}{|}_{(-2,-4,-4)}||=$

$($Simplify your answer. Type an exact answer, using radicals as needed.$)$

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}{|}_{(-2,-4,-4)}||=$

$($Simplify your answer Type an exact answer, using radicals as needed.$)$