Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle x^{3} y^{3} - 8 e^{x^{2}} \cos{\left(y^{2} \right)}=-49

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 3 x^{3} y^{2} y' + 3 x^{2} y^{3} - 16 x e^{x^{2}} \cos{\left(y^{2} \right)} + 16 y y' e^{x^{2}} \sin{\left(y^{2} \right)} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{x \left(- 3 x y^{3} + 16 e^{x^{2}} \cos{\left(y^{2} \right)}\right)}{y \left(3 x^{3} y + 16 e^{x^{2}} \sin{\left(y^{2} \right)}\right)}