Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 4 y^{3} \log{\left(x \right)} - 9 e^{x^{2}} e^{y^{2}}=14$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: - 18 x e^{x^{2}} e^{y^{2}} + 12 y^{2} y' \log{\left(x \right)} - 18 y y' e^{x^{2}} e^{y^{2}} + \frac{4 y^{3}}{x} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{9 x^{2} e^{x^{2} + y^{2}} - 2 y^{3}}{3 x y \left(2 y \log{\left(x \right)} - 3 e^{x^{2} + y^{2}}\right)}$