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

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