Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 6 x^{3} y^{3} - 8 e^{x^{3}} \sin{\left(y \right)}=14$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 18 x^{3} y^{2} y' + 18 x^{2} y^{3} - 24 x^{2} e^{x^{3}} \sin{\left(y \right)} - 8 y' e^{x^{3}} \cos{\left(y \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{x^{2} \left(- 9 y^{3} + 12 e^{x^{3}} \sin{\left(y \right)}\right)}{9 x^{3} y^{2} - 4 e^{x^{3}} \cos{\left(y \right)}}$