Question: $\displaystyle ln(x^5z^{216}) + 9 (x - 1)y + 216xz + 64y^3z = 0 $ defines $\displaystyle y$ implicitly as a function of $\displaystyle x$ and $\displaystyle z$; that is $\displaystyle y =y(x,z) $. Compute $\displaystyle \frac{\partial y}{\partial z} at (x,z) = (1,-1) $.