Calculate the partial derivatives $\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{T}}$ and $\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{U}}$ using implicit differentiation of $(TU-V{)}^{2}ln(W-UV)=ln(6)$ at $(T,U,V,W)=(5,1,6,12).$

$($Use symbolic notation and fractions where needed.$)$

$\frac{\text{d}\text{e}\text{l}\text{U}}{\text{d}\text{e}\text{l}\text{T}}=\frac{2ln(6)}{10ln(6)1}$

Incorrect Answer

$\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{U}}=\frac{10ln(6)1}{2ln(6)}$

Incorrect Answer