Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 9 x^{3} \log{\left(y \right)} + 4 y^{3} \cos{\left(x^{3} \right)}=-28$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: \frac{9 x^{3} y'}{y} - 12 x^{2} y^{3} \sin{\left(x^{3} \right)} + 27 x^{2} \log{\left(y \right)} + 12 y^{2} y' \cos{\left(x^{3} \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{x^{2} y \left(4 y^{3} \sin{\left(x^{3} \right)} - 9 \log{\left(y \right)}\right)}{3 x^{3} + 4 y^{3} \cos{\left(x^{3} \right)}}$