Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 2 x e^{y} - 7 \sin{\left(x^{2} \right)} \cos{\left(y^{3} \right)}=35$

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