Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 7 x e^{y} + 2 \sqrt{2} \sqrt{y} e^{x}=36$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: - 7 x y' e^{y} + 2 \sqrt{2} \sqrt{y} e^{x} - 7 e^{y} + \frac{\sqrt{2} y' e^{x}}{\sqrt{y}} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{- 7 \sqrt{y} e^{y} + 2 \sqrt{2} y e^{x}}{7 x \sqrt{y} e^{y} - \sqrt{2} e^{x}}$