Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 8 e^{x} e^{y} - 3 \cos{\left(x^{3} \right)} \cos{\left(y^{3} \right)}=37

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