Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 3 x y + 4 e^{x^{2}} e^{y^{2}}=36$

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