Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle - 5 \sqrt{6} \sqrt{x} \cos{\left(y \right)} - 7 y e^{x^{3}}=-13

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 5 \sqrt{6} \sqrt{x} y' \sin{\left(y \right)} - 21 x^{2} y e^{x^{3}} - 7 y' e^{x^{3}} - \frac{5 \sqrt{6} \cos{\left(y \right)}}{2 \sqrt{x}} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{42 x^{\frac{5}{2}} y e^{x^{3}} + 5 \sqrt{6} \cos{\left(y \right)}}{2 \left(- 7 \sqrt{x} e^{x^{3}} + 5 \sqrt{6} x \sin{\left(y \right)}\right)}