Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle - 9 x^{2} y^{2} - 6 \sin{\left(x^{2} \right)} \cos{\left(y^{3} \right)}=43

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