Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 2 x \log{\left(y \right)} - 9 y e^{x^{3}}=42$

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