Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle y e^{x^{2}} - 7 e^{y^{2}} \sin{\left(x^{3} \right)}=-41$

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