Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle - 3 x y + 7 e^{x^{2}} \cos{\left(y^{3} \right)}=34$

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