The equation

$2z^4=ln(e^{2z}+3xy)$

implicitly defines $z$ as a function of $x$ and $y$ in the neighborhood of the point where $x=2,y=0$ and $z=1.$

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

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

$\frac{\text{d}\text{e}\text{l}\text{z}}{\text{d}\text{e}\text{l}\text{y}}=$

Input the exact values.