Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 8 x \cos{\left(y \right)} - 6 e^{y^{3}} \log{\left(x \right)}=-33

Taking the derivative of both sides using implicit differentiation gives: LaTeX: - 8 x y' \sin{\left(y \right)} - 18 y^{2} y' e^{y^{3}} \log{\left(x \right)} + 8 \cos{\left(y \right)} - \frac{6 e^{y^{3}}}{x} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{4 x \cos{\left(y \right)} - 3 e^{y^{3}}}{x \left(4 x \sin{\left(y \right)} + 9 y^{2} e^{y^{3}} \log{\left(x \right)}\right)}