Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 18 \sqrt{y} e^{x^{2}} + 7 e^{y^{2}} \cos{\left(x^{3} \right)}=46$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: - 21 x^{2} e^{y^{2}} \sin{\left(x^{3} \right)} - 36 x \sqrt{y} e^{x^{2}} + 14 y y' e^{y^{2}} \cos{\left(x^{3} \right)} - \frac{9 y' e^{x^{2}}}{\sqrt{y}} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{3 x \left(7 x \sqrt{y} e^{y^{2}} \sin{\left(x^{3} \right)} + 12 y e^{x^{2}}\right)}{14 y^{\frac{3}{2}} e^{y^{2}} \cos{\left(x^{3} \right)} - 9 e^{x^{2}}}$