Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 6 x e^{y} - 7 y \cos{\left(x \right)}=-13$

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