Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 8 x^{3} \log{\left(y \right)} + 8 e^{x} \cos{\left(y^{3} \right)}=24$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: \frac{8 x^{3} y'}{y} + 24 x^{2} \log{\left(y \right)} - 24 y^{2} y' e^{x} \sin{\left(y^{3} \right)} + 8 e^{x} \cos{\left(y^{3} \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = - \frac{y \left(3 x^{2} \log{\left(y \right)} + e^{x} \cos{\left(y^{3} \right)}\right)}{x^{3} - 3 y^{3} e^{x} \sin{\left(y^{3} \right)}}$