Find $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}.$

$($a$)z=f(x)g(y)$

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{x}}$

$0$

$1$

$f^{\text{'}}(x)$

$g^{\text{'}}(y)$

$f^{\text{'}}(x)g(y)$

$f(x)g^{\text{'}}(y)$

$f^{\text{'}}(x)g^{\text{'}}(y)$

none of the above