Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 3 y \log{\left(x \right)} - 8 e^{x^{3}} e^{y^{3}}=12$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: - 24 x^{2} e^{x^{3}} e^{y^{3}} - 24 y^{2} y' e^{x^{3}} e^{y^{3}} + 3 y' \log{\left(x \right)} + \frac{3 y}{x} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{- 8 x^{3} e^{x^{3} + y^{3}} + y}{x \left(8 y^{2} e^{x^{3} + y^{3}} - \log{\left(x \right)}\right)}$