Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 3 x^{3} \sin{\left(y^{2} \right)} + 8 y^{3} \sin{\left(x^{2} \right)}=28

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 6 x^{3} y y' \cos{\left(y^{2} \right)} + 9 x^{2} \sin{\left(y^{2} \right)} + 16 x y^{3} \cos{\left(x^{2} \right)} + 24 y^{2} y' \sin{\left(x^{2} \right)} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = - \frac{x \left(9 x \sin{\left(y^{2} \right)} + 16 y^{3} \cos{\left(x^{2} \right)}\right)}{6 y \left(x^{3} \cos{\left(y^{2} \right)} + 4 y \sin{\left(x^{2} \right)}\right)}