Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 9 x y - 4 e^{y^{2}} \sin{\left(x^{2} \right)}=-21$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 9 x y' - 8 x e^{y^{2}} \cos{\left(x^{2} \right)} - 8 y y' e^{y^{2}} \sin{\left(x^{2} \right)} + 9 y = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{8 x e^{y^{2}} \cos{\left(x^{2} \right)} - 9 y}{9 x - 8 y e^{y^{2}} \sin{\left(x^{2} \right)}}$