Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 6 x^{2} \sin{\left(y \right)} - 5 \sqrt{y} e^{x}=2$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 6 x^{2} y' \cos{\left(y \right)} + 12 x \sin{\left(y \right)} - 5 \sqrt{y} e^{x} - \frac{5 y' e^{x}}{2 \sqrt{y}} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{2 \left(- 12 x \sqrt{y} \sin{\left(y \right)} + 5 y e^{x}\right)}{12 x^{2} \sqrt{y} \cos{\left(y \right)} - 5 e^{x}}$