Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 3 y \cos{\left(x^{2} \right)} - 7 e^{x^{3}} \cos{\left(y^{2} \right)}=5$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: - 21 x^{2} e^{x^{3}} \cos{\left(y^{2} \right)} + 6 x y \sin{\left(x^{2} \right)} + 14 y y' e^{x^{3}} \sin{\left(y^{2} \right)} - 3 y' \cos{\left(x^{2} \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{3 x \left(7 x e^{x^{3}} \cos{\left(y^{2} \right)} - 2 y \sin{\left(x^{2} \right)}\right)}{14 y e^{x^{3}} \sin{\left(y^{2} \right)} - 3 \cos{\left(x^{2} \right)}}$