Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 5 e^{x} e^{y} + 9 \sin{\left(y^{2} \right)} \cos{\left(x \right)}=-5$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 18 y y' \cos{\left(x \right)} \cos{\left(y^{2} \right)} - 5 y' e^{x} e^{y} - 5 e^{x} e^{y} - 9 \sin{\left(x \right)} \sin{\left(y^{2} \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{5 e^{x + y} + 9 \sin{\left(x \right)} \sin{\left(y^{2} \right)}}{18 y \cos{\left(x \right)} \cos{\left(y^{2} \right)} - 5 e^{x + y}}$