Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 5 x^{2} \log{\left(y \right)} - 8 y^{2} \cos{\left(x^{3} \right)}=-23$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 24 x^{2} y^{2} \sin{\left(x^{3} \right)} + \frac{5 x^{2} y'}{y} + 10 x \log{\left(y \right)} - 16 y y' \cos{\left(x^{3} \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = - \frac{2 x y \left(12 x y^{2} \sin{\left(x^{3} \right)} + 5 \log{\left(y \right)}\right)}{5 x^{2} - 16 y^{2} \cos{\left(x^{3} \right)}}$